CHAPTER 5 : THE STRAIGHT LINE

Similar documents
b UVW is a right-angled triangle, therefore VW is the diameter of the circle. Centre of circle = Midpoint of VW = (8 2) + ( 2 6) = 100

ANALYTICAL GEOMETRY Revision of Grade 10 Analytical Geometry

(b) the equation of the perpendicular bisector of AB. [3]

Downloaded from

Chapter 10 Exercise 10.1

Preface. Enhanced Learning

MEP Pupil Text 13-19, Additional Material. Gradients of Perpendicular Lines

Vectors Practice [296 marks]

Skills Practice Skills Practice for Lesson 9.1

Part (1) Second : Trigonometry. Tan

CSSTP. Given CSSTP. Statements Reasons. Given CSSTP. Mult. Prop. = Div. Prop. = Sym. Prop. = or 1 Mult. Prop. = Div. Prop. =

1-2 Measuring and Constructing Segments

1 k. cos tan? Higher Maths Non Calculator Practice Practice Paper A. 1. A sequence is defined by the recurrence relation u 2u 1, u 3.

NAME: Date: HOMEWORK: C1. Question Obtained. Total/100 A 80 B 70 C 60 D 50 E 40 U 39

Circles, Mixed Exercise 6

Midterm Study Guide Assessment. Question 1. Find the angle measure. (28x + 14) (16x + 62) The measure of the angles are. 11/30/2018 Print Assignment

chapter 1 vector geometry solutions V Consider the parallelogram shown alongside. Which of the following statements are true?

6. COORDINATE GEOMETRY

CfE Higher Mathematics Course Materials Topic 2: Vectors

VECTORS Contents Page 7.0 Conceptual Map Introduction to Vector Practice Multiplication of Vector y Scalar Practice Practice 7.2

y hsn.uk.net Straight Line Paper 1 Section A Each correct answer in this section is worth two marks.

9.2. Length of Line Segments. Lesson Objectives. Find the lengths of line segments on the x-axis and y-axis.

"Full Coverage": Vectors

Year 11 Math Homework

Algebraic Expressions

MT - GEOMETRY - SEMI PRELIM - I : PAPER - 2

1 What is the solution of the system of equations graphed below? y = 2x + 1

Applications. 12 The Shapes of Algebra. 1. a. Write an equation that relates the coordinates x and y for points on the circle.


Mathematics. Exercise 6.4. (Chapter 6) (Triangles) (Class X) Question 1: Let and their areas be, respectively, 64 cm 2 and 121 cm 2.

Honors Geometry Mid-Term Exam Review

TRIANGLE EXERCISE 6.4

Chapter 1 Coordinates, points and lines

Practice Test Geometry 1. Which of the following points is the greatest distance from the y-axis? A. (1,10) B. (2,7) C. (3,5) D. (4,3) E.

8. Quadrilaterals. If AC = 21 cm, BC = 29 cm and AB = 30 cm, find the perimeter of the quadrilateral ARPQ.

COORDINATE GEOMETRY BASIC CONCEPTS AND FORMULAE. To find the length of a line segment joining two points A(x 1, y 1 ) and B(x 2, y 2 ), use

Created by T. Madas 2D VECTORS. Created by T. Madas

Geometry Essentials ( ) Midterm Review. Chapter 1 For numbers 1 4, use the diagram below. 1. Classify as acute, obtuse, right or straight.

Conditional Statement: Statements in if-then form are called.

5-1 Perpendicular and Angle Bisectors

Visit: ImperialStudy.com For More Study Materials Class IX Chapter 12 Heron s Formula Maths

JUST IN TIME MATERIAL GRADE 11 KZN DEPARTMENT OF EDUCATION CURRICULUM GRADES DIRECTORATE TERM

Topic 2 [312 marks] The rectangle ABCD is inscribed in a circle. Sides [AD] and [AB] have lengths

Chapter 3 Summary 3.1. Determining the Perimeter and Area of Rectangles and Squares on the Coordinate Plane. Example


Grade 9 Quadrilaterals

Chapter 20 Exercise 20.1

Year 9 Term 3 Homework

b) What is the area of the shaded region? Geometry 1 Assignment - Solutions

Similarity. Question Paper 2. Save My Exams! The Home of Revision. Shape, Space and Measures. Booklet Question Paper minutes.

Which statement is true about parallelogram FGHJ and parallelogram F ''G''H''J ''?

VAISHALI EDUCATION POINT (QUALITY EDUCATION PROVIDER)

1-2 Measuring and Constructing Segments

G.GPE.B.4: Quadrilaterals in the Coordinate Plane 2

1. In a triangle ABC altitude from C to AB is CF= 8 units and AB has length 6 units. If M and P are midpoints of AF and BC. Find the length of PM.

Geometry Honors: Midterm Exam Review January 2018

Shape Booster 6 Similar Shapes

Math : Analytic Geometry

SECTION A(1) k k 1= = or (rejected) k 1. Suggested Solutions Marks Remarks. 1. x + 1 is the longest side of the triangle. 1M + 1A

Thursday 11 June 2015 Afternoon

St Andrew s Academy Mathematics Department Higher Mathematics VECTORS

Test Corrections for Unit 1 Test

Paper Reference. Ruler graduated in centimetres and millimetres, protractor, compasses, pen, HB pencil, eraser. Tracing paper may be used.

Q.2 A, B and C are points in the xy plane such that A(1, 2) ; B (5, 6) and AC = 3BC. Then. (C) 1 1 or

LESSON 2 5 CHAPTER 2 OBJECTIVES

CBSE Sample Paper-03 (Unsolved) SUMMATIVE ASSESSMENT II MATHEMATICS Class IX. Time allowed: 3 hours Maximum Marks: 90

VIII - Geometric Vectors

Day 31 Bellringer. (a) 2 and 7. (b) 3 and 7. (c) 3 and 6. Page 1

1-2 Measuring and Constructing Segments


Vectors. Paper 1 Section A. Each correct answer in this section is worth two marks. 4. The point B has coordinates

PYTHAGORAS THEOREM PYTHAGORAS THEOREM IN A RIGHT ANGLED TRIANGLE, THE SQUARE ON HYPOTENUSE IS EQUAL TO SUM OF SQUARES ON OTHER TWO SIDES

0110ge. Geometry Regents Exam Which expression best describes the transformation shown in the diagram below?

Grade 11 November Examination 2015 Mathematics: Paper 2 Time: 3 hours Marks: 150

PREPARED BY: ER. VINEET LOOMBA (B.TECH. IIT ROORKEE) 60 Best JEE Main and Advanced Level Problems (IIT-JEE). Prepared by IITians.

Distance. Warm Ups. Learning Objectives I can find the distance between two points. Football Problem: Bailey. Watson

DATE: MATH ANALYSIS 2 CHAPTER 12: VECTORS & DETERMINANTS

Mathematics. Exercise 9.3. (Chapter 9) (Sequences and Series) Question 1: Find the 20 th and n th terms of the G.P. Answer 1:

ANSWER KEY. LEARNING ACTIVITY 1 Challenge a. A + B = (The sum of its adjacent interior angles between two parallel sides is + B = B = B =

MT - GEOMETRY - SEMI PRELIM - I : PAPER - 4

GR 11 MATHS ANALYTICAL GEOMETRY

Proofs Practice Proofs Worksheet #2

Maharashtra State Board Class X Mathematics - Geometry Board Paper 2016 Solution

CBSE Class IX Mathematics Term 1. Time: 3 hours Total Marks: 90. Section A

KENDRIYA VIDYALAYA GACHIBOWLI, GPRA CAMPUS, HYD 32

2. A diagonal of a parallelogram divides it into two congruent triangles. 5. Diagonals of a rectangle bisect each other and are equal and vice-versa.

MT - GEOMETRY - SEMI PRELIM - I : PAPER - 1

MHR Principles of Mathematics 10 Solutions 1

( 1 ) Find the co-ordinates of the focus, length of the latus-rectum and equation of the directrix of the parabola x 2 = - 8y.

iii (a, c), (a, e), (c, e), (b, d), (b, f), (d, f), (l, h), (l, j), (h, j), (g, i), (g, k), (i, k)

Geometry Honors Review for Midterm Exam

STRAIGHT LINES EXERCISE - 3

How could you express algebraically, the total amount of money he earned for the three days?

AREAS OF PARALLELOGRAMS AND TRIANGLES

SQA Higher Mathematics Unit 1

5 Find an equation of the circle in which AB is a diameter in each case. a A (1, 2) B (3, 2) b A ( 7, 2) B (1, 8) c A (1, 1) B (4, 0)

UNIT 1: SIMILARITY, CONGRUENCE, AND PROOFS. 1) Figure A'B'C'D'F' is a dilation of figure ABCDF by a scale factor of 1. 2 centered at ( 4, 1).

Chapter (Circle) * Circle - circle is locus of such points which are at equidistant from a fixed point in

St Andrew s Academy Mathematics Department Higher Mathematics

Triangles. Example: In the given figure, S and T are points on PQ and PR respectively of PQR such that ST QR. Determine the length of PR.

Transcription:

EXERCISE 1 CHAPTER 5 : THE STRAIGHT LINE 1. In the diagram, PQ is a straight line. P 4 2 4 3 2 1 0 1 2 2 2. Find (a) the -intercept, (b) the gradient, of the straight line. Q (5,18) Q Answer :a).. b) 3 P 0 Find a) the gradient of PQ b) the equation of straight line PQ Answer :a) b) 3. Determine the gradient of the straight line = 9 4 + 4. F Answer : E(-2,6) 0 G 5. The Determine diagram shows the -intercept two straight of the lines, straight EF and line FG, 2 on a = Cartesian - plane. The gradient of EF is 1 and the distance of FG is 10 units. The -intercept of FG is 38 Answer :.

6. The gradient of the straight line 2 + 6 = 13 Answer :... 7. The - intercept of the straight line 4 2 = 12 is 8. In the diagram, AB is a straight line. Answer : A -12 0-3 B What is the gradient of AB? 9. In the diagram, R = S. The equation of RS is Answer :.. S R -4 0 10. In the diagram, MLT is a right-angled triangle.. L(6,7) Answer: M T(6,4) 0 Find a) the coordinate of M, b) the equation of the straight line LT. Answer :.a)... b). 39

EXERCISE 2 CHAPTER 5 : THE STRAIGHT LINE 1. P Q (3,5) R The diagram shows a parallelogram PQR. Given that the gradient of P = - 3 5. The -intercept of line QR is... Answer : 2. Q(0,5) R(12,3) P 0 S(4,k) In the diagram, PQRS is a parallelogram. The equation of the straight line RS is 2 = 6. Find a) the value of k, b) the gradient of the straight line QR, Answer: a) b). 40

3. In the diagram, PQR is a parallelogram and is the origin. Find a) the gradient of the straight line R, b) the equation of the straight line PQ Q R(2,4) P(6,1) 0 Answer: a) b). 4. In the diagram PQRS is a parallelogram P(-2,12) Q S 0 a) Given that the gradient of line PQ is -3, find the equation of PQ b) Find the coordinate of point R. R Answer a)... b)... 41

5. In the diagram, LH is a straight line. Given that the gradient of the straight line LH is -1. L(-3,9) H(0,k) Find (a) the value of k, (b) the equation of the stragiht line LH. 0 Answer: a) b). 6. In the diagram above, ABCD is a parallelogram and is the origin. The straight line BD is parallel with the -ais and the equation of line AB is = 3 2 + 4. B(6,10) A C Find (a) the -intercept of the straight line AB, (b) the gradient of AD, 0 D Answer: a) b) 42

Q(4,8) S(10,2) 0 P(2,0) R 7. In the diagram, PQ is parallel to RS and is the origin. Find a) the gradient of RS b) the - intercept of RS Answer: a) b) 8. In the diagram M = 3 1 A and the length of the straight line A is 9 units. A B 0 M (a) Find the coordinate of point B. (b) Calculate the gradient of line MB. Answer a)... b)... 43

9. In the diagram, CD is parallel to EF. D = 3+5 F 0 C Find (a) the -intercept of line CD, (b) the equation of straight line EF. E(-1,-4) Answer: a) b) 10. In the diagram, EFGH is a parallelogram. Given that the gradient of line EF is 2 5. Find the coordinate of point G. E H(8,5). F 0 G Answer: 44

DIAGNSTIC TEST CHAPTER 5 : THE STRAIGHT LINE 1. In Diagram 1, MN is a straight line. M 6 0 8 N Diagram 1 Find the gradient of MN. A -2 3 B 4 3 C - 4 D 2 2. Given that the equation of a straight line is 2 + 3 = 0. Find the -intercept of the straight line. A -1 B -2 C -3 D -4 3. In Diagram 2, the length of C is 2 units. B A(10,6) C Diagram 2 The gradient of line BC is A 3 B 4 C -4 45

D -3 P(8,2) R(-2,-8) Diagram 3 4. Based on Diagram 3, find the equation of line PR. A = - 6 B = - + 6 C = + 6 D = 6 5. In Diagram 4, the equation of the line WZ is = 4 3. Q (8, k) is a point on the line WZ. W Q (8, k) Diagram 4 Z 0 Find the value of k. A 6 B 7 C 8 D 9 6. The equation of a straight line passing through the point ( -3, 8 ) and parallel to the line = 3 2 + 5 is A = 3 2 + 8 B 3 = 2 + 10 C 3 = 2 + 30 D = 3 2-3 46

E Diagram 5 0 G 7. In Diagram 5, E = G. Find the gradient of line EG. A 1 B -1 C 2 D -2 U(-3,6) Diagram 6 0 8. In Diagram 6, find the gradient of the line U. A 1 B -1 C 2 D -2 9. The -intercept of the straight line 4 = 3 2 is 3 A 4 1 B - 2 C - 4 3 D 1 2 47

R J ( 4, 8 ) Diagram 7 0 P 10. In Diagram 7, the length of P is 10 units. The equation of line PR is 4 A = + 8 5 4 B = - + 8 5 5 C = +4 4 5 D = - + 4 4 48

CHAPTER 5 : THE STRAIGHT LINE EXERCISE 1 1. R(5,7) Q(1,4) P(-1,0) S Diagram 1 In Diagram 1, straight lines PQ and RS are parallel. Find the a) gradient of the line PQ, b) equation of the line RS, c) -intercept of the line RS. 2.. N K M(5,0) L Diagram 2 In Diagram 2, straight lines KL and MN are parallel. The equation of the line KL is + 3 + 3 = 0. Find the a) gradient of the line KL, b) equation of the line MN, c) -intercept of the line MN. 49

3. F(3,k) G(7,10) E H Diagram 3 In Diagram 3, straight line FG is parallel to the -ais while the lines EF and GH are parallel. The gradient of the line EF is 2. a) State the value of k, b) Find the equation of the line GH, c) Find the coordinates of the point E. 4. M (5,20) L K Diagram 4 In Diagram 4, KLM is a parallelogram and line ML is parallel to the -ais.point L is on the -ais. a) State the coordinates of the point L, b) Find the -intercept of the line KL, c) Find the equation of the line KL. 50

5. V(8, k) U T(-2,1) S W Diagram 5 In Diagram 5, the equation of the straight line STUV is 2 = + 4. The lines T and UW are parallel. Find the a) value of k, b) -intercept of the line STUV, c) equation of the line UW. 51

EXERCISE 2 1. CHAPTER 5 : THE STRAIGHT LINE B(-3,10) C A Diagram 1 The equation of the straight line AB in Diagram 1 is = 2 +16. a) State the equation of the straight line BC, b) Find the -intercept of the straight line AB, c) Find the equation of AC. U Y Z (6,5) C (-2,3) V D (8,-2) 2. Diagram 2 In Diagram 2, the straight line UV is parallel to CD. is the origin. a) Calculate the gradient of line CD, b) Find the equation of line UZV, c) Find - intercept of line UZV. 52

3. Q (h, 3 ) R P( -8, 0 ) 0 S ( 6, 0 ) Diagram 3 In Diagram 3, the gradient of the straight line PQR is 3.Find the a) value of h b) -intercept of the line RS c) equation of the line RS 4. B (2, 8 ) C A (2, 3 ) 0 Diagram 4 In Diagram 4, ABC is a parallelogram. Find the a) coordinates of C b) equation of the straight line BC 53

5. Y Q S 12 P -4 3 X R Diagram 5 In Diagram 5, straight lines PQ and RS are parallel. a) State the gradient of PQ b) Find the equation of RS c) Find the intercept of RS 54

CHAPTER 5 : THE STRAIGHT LINE DIAGNSTIC TEST 1. A B (6, 5) D C (6, 0) Diagram 1 In Diagram 1, A and D are located on the -ais and ABCD is a parallelogram. If the gradient of AB = - 2 1, a) State the gradient of CD. b) Determine the coordinates of D. c) Find the equation of the straight line AB. [ 5 marks ] 2. P (0, 9) Q (5, 7) R (0, -5) Diagram 2 Diagram 2 shows a triangle PQR. a) State the -intercept of the straight line PQ, b) Find the equation of the straight line QR, c) Find the equation of a straight line that passes through P and parallel to the straight line QR. [ 5 marks ] 55

3. M P Diagram 3 N In Diagram 3, MN = 12 units and parallel to the -ais. Given N = 6 units and P = 3 2 MN, 4. a) State the coordinates of P, b) Find the gradient of the straight line PM, c) Find the equation of the straight line PM. A D = 2 + k [ 5 marks ] C E B Diagram 4 In Diagram 4, two straight lines AB and CD intersect at point (-1, 3). Given the gradient of AB is -1, find the a) value of k, b) equation of the straight line AB, c) coordinates of point E. [ 5 marks] 56

5. P (-3, 6) Q (h, k) M (4, 3) Diagram 5 R In Diagram 5, Q and PR intersect at M which is midpoint of Q. Given is the origin. Find a) the value of h and k, b) the equation of the straight line PR. [ 5 marks] 57