IMSA Name: GEOMETRY I/II DUE: Tues., Oct. 27 Problem Set #9 (Spring MI-2 Students) Show all work and justifications neatl. Be sure I can follow our steps. EXACT answers, unless specified. Also, be sure ou do the correct set of MI-2/MI-3 problems. 1. The equation for a circle with center (0, 0) and radius R is 2 + 2 = R 2. The equation for a circle with center (h, k) and radius r is ( h) 2 + ( k) 2 = r 2. a. Find the center and radius of the circle whose equation is as follows: (i) 2 + 2 = 36 (ii) ( + 4) 2 + ( 7) 2 = 12 b. Find the center and radius of the circle whose equation is as follows. You will need to complete the square to put the following equation in the proper form. 2 + 10 + 2 6 = 11 (Hint: 2 + 10 + + 2 6 + = 11 + + ) c. Write the equation of the circle if a diameter of the circle has endpoints at A( 4, 5) and B(6, 2). 2. Given: V = l w h. a. If l and w are each doubled, and h is triples, how will V change? Justif our answer. b. If l is quadrupled, h is reduced b half, and w is reduced b a factor of si, how will V change? Justif our answer. 3. Suppose m n and PQ and RQ bisect the angles in the figure at the right. Using a combination of algebra and some well-chosen facts and theorems, find the measure of Q. Be sure to state the facts or theorems ou use to find this measure. 4. The legs of a trapezoid are 17 and 25 while the shorter base is 30 and the height is 15. Find the longer base and the lengths of both diagonals. NOTE: There are reall two cases for ou to consider here. (A drawing for each case would be helpful.) n m R P j Q 5. Given the figure shown at the right: a. Find the lateral area and total area of the figure if the height, h, is 16. b. Find the height, h, if the lateral area of the figure is 754. 12 9 25 12 h Top View 9 12 12 25 6. The shaded area in the figure at the right is 54. Find the radii of the large semicircle and each of the three identical small semicircles. Prob Set 9.1
7. A semicircle is mounted on the side of an equilateral triangle as shown in the figure at the right. If the length of the side of the equilateral triangle is 12 cm, find each of the following. a. the perimeter of the entire region b. the area of the entire region 8. One of the numbers from the set {1, 2, 3, 4,..., 100} is chosen at random. What is the probabilit that this number is a solution to the inequalit 2 + 10 144? 9. A biccle has 30 diameter wheels. Find the distance that the biccle moves forward after eight revolutions of the wheel on the ground. How man revolutions would a 24 biccle wheel have to make to move forward the same distance? 10. Suppose the points A( 8, 2), B( 4, 4), and C(16, 6) are the vertices of a triangle. a. Find the equation of the perpendicular bisector of AB. Call this line m. b. Find the equation of the perpendicular bisector of BC. Call this line n. c. Find the equation of the perpendicular bisector of AC. Call this line p. d. Use the equations from parts (a) and (b) to find the point of intersection of lines m and n. e. Use the equations from parts (a) and (c) to find the point of intersection of lines m and p. f. Based on the results of parts (d) and (e), write a conjecture about the perpendicular bisectors of the sides of a triangle. SECTION DESIGNATED FOR SPRING MI-2 GEOMETRY STUDENTS 2 5 6 II-1. When is the epression : 2 2 6 a. undefined? b. equal to zero? II-2. Simplif completel. 12 a. 3 9 II-3. Solve for : a. 2 1 6 2 9 3 27 b. b. 22 4 5 2 4 5 2 6 6 6 6 II-4. Solve for in terms of : 3 2 5 3 4 Prob Set 9.2
GEOMETRY I/II Student Number: DUE: Tues., Oct. 27 Mods: Keton Porzio Problem Set #9 (Spring MI-2 Students) Remember to clearl bo our final answers. 1a. (i) 2 + 2 = 36 1b. 2 + 10 + 2 6 = 11 Center is: Radius is: 2 + 10 + + 2 6 + = 11 + + (ii) ( + 4) 2 + ( 7) 2 = 12 Center is: Radius is: 1c. 2a. Center is: Radius is: 2b. 3. m P j Q n R Prob Set 9.1
Remember to clearl bo our final answers. On the MI-2 preparation problems, show our work and organize our problems in a clear manner. 4. 5a. Lateral Area: 5b. Total Area: 6. 7a. 7b. Prob Set 9.2
Remember to clearl bo our final answers. On the MI-2 preparation problems, show our work and organize our problems in a clear manner. 8. 9. 10a. 10b. 10c. 10d. 10e. 10f. Prob Set 9.3
Remember to clearl bo our final answers. On the MI-2 preparation problems, show our work and organize our problems in a clear manner. II-1. II-2. II-3. II-4. Prob Set 9.4
IMSA Name: GEOMETRY I/II DUE: Tues., Oct. 27 Problem Set #9 (Spring MI-3 Students) Show all work and justifications neatl. Be sure I can follow our steps. EXACT answers, unless specified. Also, be sure ou do the correct set of MI-2/MI-3 problems. 1. The equation for a circle with center (0, 0) and radius R is 2 + 2 = R 2. The equation for a circle with center (h, k) and radius r is ( h) 2 + ( k) 2 = r 2. a. Find the center and radius of the circle whose equation is as follows: (i) 2 + 2 = 36 (ii) ( + 4) 2 + ( 7) 2 = 12 b. Find the center and radius of the circle whose equation is as follows. You will need to complete the square to put the following equation in the proper form. 2 + 10 + 2 6 = 11 (Hint: 2 + 10 + + 2 6 + = 11 + + ) c. Write the equation of the circle if a diameter of the circle has endpoints at A( 4, 5) and B(6, 2). 2. Given: V = l w h. a. If l and w are each doubled, and h is triples, how will V change? Justif our answer. b. If l is quadrupled, h is reduced b half, and w is reduced b a factor of si, how will V change? Justif our answer. 3. Suppose m n and PQ and RQ bisect the angles in the figure at the right. Using a combination of algebra and some well-chosen facts and theorems, find the measure of Q. Be sure to state the facts or theorems ou use to find this measure. 4. The legs of a trapezoid are 17 and 25 while the shorter base is 30 and the height is 15. Find the longer base and the lengths of both diagonals. NOTE: There are reall two cases for ou to consider here. (A drawing for each case would be helpful.) n m R P j Q 5. Given the figure shown at the right: a. Find the lateral area and total area of the figure if the height, h, is 16. b. Find the height, h, if the lateral area of the figure is 754. 12 9 25 12 h Top View 9 12 12 25 6. The shaded area in the figure at the right is 54. Find the radii of the large semicircle and each of the three identical small semicircles. Prob Set 9.1
7. A semicircle is mounted on the side of an equilateral triangle as shown in the figure at the right. If the length of the side of the equilateral triangle is 12 cm, find each of the following. a. the perimeter of the entire region b. the area of the entire region 8. One of the numbers from the set {1, 2, 3, 4,..., 100} is chosen at random. What is the probabilit that this number is a solution to the inequalit 2 + 10 144? 9. A biccle has 30 diameter wheels. Find the distance that the biccle moves forward after eight revolutions of the wheel on the ground. How man revolutions would a 24 biccle wheel have to make to move forward the same distance? 10. Suppose the points A( 8, 2), B( 4, 4), and C(16, 6) are the vertices of a triangle. a. Find the equation of the perpendicular bisector of AB. Call this line m. b. Find the equation of the perpendicular bisector of BC. Call this line n. c. Find the equation of the perpendicular bisector of AC. Call this line p. d. Use the equations from parts (a) and (b) to find the point of intersection of lines m and n. e. Use the equations from parts (a) and (c) to find the point of intersection of lines m and p. f. Based on the results of parts (d) and (e), write a conjecture about the perpendicular bisectors of the sides of a triangle. SECTION DESIGNATED FOR SPRING MI-3 GEOMETRY STUDENTS III-1. Find the determinant of the following matri (show our work): III-2. Solve and graph on a number line: 3 4 7 III-3. Given the function () = 2 + 3 10, complete the following. 8 5 3 2 a. Find (2) b. Find (3) c. Find the value(s) of k so that (k) = 8. III-4. Suppose and are given b the following parametric equations: 2 t 2 a. If 7 t 2, find the resulting range of values for and on. b. Eliminate the parameter, t, to come up with an equation for in terms of. c. Graph the equation ou found in part (b) for all t in the domain indicated in (a). Label all important features in our graph. 2 t Prob Set 9.2
GEOMETRY I/II Student Number: DUE: Tues., Oct. 27 Mods: Keton Porzio Problem Set #9 (Spring MI-3/4 Students) Remember to clearl bo our final answers. 1a. (i) 2 + 2 = 36 1b. 2 + 10 + 2 6 = 11 Center is: Radius is: 2 + 10 + + 2 6 + = 11 + + (ii) ( + 4) 2 + ( 7) 2 = 12 Center is: Radius is: 1c. 2a. Center is: Radius is: 2b. 3. m P j Q n R Prob Set 9.1
Remember to clearl bo our final answers. On the MI-3 preparation problems, show our work and organize our problems in a clear manner. 4. 5a. Lateral Area: 5b. Total Area: 6. 7a. 7b. Prob Set 9.2
Remember to clearl bo our final answers. On the MI-3 preparation problems, show our work and organize our problems in a clear manner. 8. 9. 10a. 10b. 10c. 10d. 10e. 10f. Prob Set 9.3
Remember to clearl bo our final answers. On the MI-3 preparation problems, show our work and organize our problems in a clear manner. III-1. III-2. III-3. III-4. Prob Set 9.4