Chapter 20 Exercise 20.1

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1 Chapter Eercise. Q.. (i B = (, A = (, (ii C (, + = (, (iii AC ( + ( ( + ( 9 + CB ( + + ( ( + ( 9 + AC = CB (iv Slope of AB = = = = ( = ( = + + = (v AB cuts the -ais at =. + = = = AB cuts the -ais at (,. (vi h = base = Area = b h = C = (, Q.. (i (vi AB cuts the -ais at = + ( = = = AB cuts the -ais at (,. A = (, C = (, B = (, (ii M (, + = M(, (iii AB: slope = = = (iv = ( = + + = (v + = = = = + = = (, = units A = (, B = (, Active Maths (Strands : Ch Solutions

2 Q.. (i m: + = = + = + Slope =, C = m n (ii n: = = + = Slope =, C = m (, n (, (iii + = + + = = = = = = = (, (iv At -ais, = + = = = (, Active Maths (Strands : Ch Solutions

3 Q.. (i + = = = + Slope =, C = + = = + Slope =, C = 7 s 9 7 r 7 9 (ii 7 s 9 7 r (, 7 9 (, (iii + = + = 7 7 = 7 = 7 = ( + = = = (, (iv At -ais, = + = = = (, Active Maths (Strands : Ch Solutions

4 Q.. (i + = = + = + 9 Slope =, c = 9 = Slope =, c = (ii (, p q p q (, (iii + = + ( = + = 9 = = = = ( = (, Q.. (i d ( + + ( + + _ = units (ii = km (iii T = D S =. = hr = minutes Q. 7. (i h: + = (, ( + =? + =? = (, h (ii (k, (k + = k = (iii Let = + = = = (, Let = = = = (, Let = k = + = = = (, (iv Slope = + = = (v + = = + m = Q.. (i = (ii = + Q. 9. (, (, (, a = b = Q.. (i m = = = = ( = + = + l : + = Active Maths (Strands : Ch Solutions

5 (ii l : = + + = (iii + = + ( = = (c D = (, A = (, C = (, B = (, 7 = = 7 = ( 7 = 7 ( 7, 7 Midpoint ( 7, + 7 = (, Q.. (a A(, (b B(, = ( 7, A = (, 7 D = (, B = (, (d (, D = (, A = (, C = (, B = (, (, (e AD ( + ( ( + ( BD ( + ( ( + ( (f ABD is an isosceles Δ as two sides are equal in measure. (g AD = BD shown in (e AC = BC as C is the midpoint CD = CD as it is the common side Δ ACD Δ BCD b SSS. Q.. (i D = (, C = (,9 A = (, B = (, Active Maths (Strands : Ch Solutions

6 (ii AD ( + ( ( + ( + 9 BC ( + (9 ( + ( + 9 AD = BC (iii Midpoint of [AC]: E ( +, + 9 Midpoint of [BD] F ( +, + E = F = (, = (7, = (, = (7, [AC] and [BD] bisect each other. (iv Yes, I can now conclude that ABCD is a parallelogram as opposite sides are equal in length and the diagonals bisect each other. Eercise. Q.. Slope Slope of parallel line Q.. Slope of perpendicular line _ _ _ _ _ Q.. Q.. (ii + = (iii = 9 = = + m = = + 9 = 9 m = (iv ( = = = + = m = (v ( = + = = = + m = (vi = = + = + m = Q.. + = = + m = c = Line + = has m = Equation is = + = + Q. 9. = = + = m =, c = Q.. Q.. Q. 7. (i + = = + m = Active Maths (Strands : Ch Solutions Line to = has slope = = + + =

7 Q.. + = = + = + m =, c = Slope of line to + = is = + Q.. + = = = + b: + = = = + = m a b (iii a: = = + = b: + = = m =, c = Line to + = has slope = ( = + = Q = = = m =, c = Line to + + = has slope + = ( + = = Q.. (i a: + = = + = + b: + = = = + m = ( ( a b (ii a: + = = + = + = + = m a b (iv a: = = + = b: = + m = ( ( = a b (v a: + = = + = + b: = + = + m = ( ( a b (vi a: = 7 b: + = = + = + m = ( ( = a b Q.. (i (, = is horizontal, Line to = must be vertical. Vertical line going through (, has equation =. Active Maths (Strands : Ch Solutions 7

8 (ii It is not possible to verif as slope of = is and slope of = is undefined. Q.. l: + = = = + m = Slope of k = + = ( + = = Q.. m: + = = = + n has slope = ( + = + + = Q. 7. p: 7 + = = 7 = 7 + q has slope 7 = 7( + = = Q.. l: + = = = + k has slope = ( = + + = Revision Eercises Q.. (i m = rise run = (ii C ( +, + = ( _, (iii AB ( + ( ( + ( + (iv Slope of k = C ( _, = ( 7 = + = + k: + 7 = (v At -ais, = 7 = = 7 =.7 (.7, At -ais, = 7 = = 7 = 7 (, 7 Q.. (i l: + 7 = P(,h: ( (h + 7 = m: + = h + 7 = h + = h = h = Q(k,: (k + ( = k = k = k = Active Maths (Strands : Ch Solutions

9 (ii + 7 = + = 9 + = + 9 = 7 = = 7 = (iii + 7 = ( + 7 = = l = = (, m R = (, P = (, Q = (, (iv PRQ is a right angle PR RQ l m l: + 7 = = 7 = + 7 m: + = = + = + m = ( ( = l m PRQ is a right angle. Q.. (i P(, R(, M ( +, + (ii m = = M (, = M(, ( = = (iii Line to [PR] has slope = ( = + + = (iv k: = l: + = = + = = = = = = = N(, Q.. l: + = (i = = Slope of k = = ( = 9 k: = (ii k and l are + = = + = 9 = = = + = ( + = = = Point of intersection of k and l is (, P (, (, P (, Active Maths (Strands : Ch Solutions 9

10 Q.. (i AD: = ( BC: m = ( = + = = = + = = m = ( = AD BC (ii BC ( + ( ( ( + ( + 9 (iii Area of ΔABC = b h = = 9 = 9 = units Q.. (i l: + = At -ais, = + = = = (, = C m: + = = = = D = (, (ii + = + + = = 9 = 7 = ( + = + = = = E = (, (iii E = (, C = (, D = (, (iv Area ΔCDE = b h Q. 7. (i R (, + = 9 = 7 =. units = R (, = R(, (ii Slope PQ = ( = + = = Slope of k = k: + = ( + = k: = (iii k: = S(, =? = S k (iv If ΔPQS is isosceles then PS = QS PS ( + ( ( + ( + QS ( + ( ( + ( + ΔPQS is isosceles Active Maths (Strands : Ch Solutions

11 Q.. (a Slope of l = rise run = 7 = = Slope of l = rise run = = 7 =. (b At a stead speed of km/hr John s car can travel km per litre of fuel consumed and at a stead speed of km/hr John s car travels. km per litre of fuel consumed. (c At km/hr: 9.9 =,7 c = 7. At km/hr:. 9.9 =,7 7 c = =. cheaper Q. 9. (a Line has greatest slope as slope = (b Lines and are parallel as the both have slope. (c (d It represents line. (e Line (f = 7 = + = = = = 7 = (, (g Line : If =, = 7 = Line : If =, = ( = = Active Maths (Strands : Ch Solutions

12 Q.. (a A(, (b A = (, D = (, E = (, B = (, C = (, F = (, (c Midpoint [DF] = ( +, (d Slope BF = rise run = = intercept BF = D = = (, = (, BF: = + (e Slope CE = rise run = = (f = ( + = + + = (g Area ΔBCE : Area ΔBCF : (h Yes, ΔBCE and ΔBCF are congruent because the have equal area, BE = CF and EC = BF Q.. (i k: + = At -ais, = + = = A (, = At -ais, = + = B (, = = (ii m A = (, k B = (, (iii k: + = = = + Slope of m = m: = ( = m: + = Q.. (i + = + = + = = = + = + = = = R (, (ii k: + = Q (,: + =? = Q k (iii QR ( + ( ( + ( = Q.. (i + = + = + = = = + = + = = = R (, Active Maths (Strands : Ch Solutions

13 (ii a: + = At -ais, = = = Q (, (iii b: + = At -ais, = + = = = P (, (iv 9 a 7 R = (, P = (, b Q = (, (v T ( +, + (vi Slope PT = slope PQ = -intercept = = m + c = + = + + = Q.. Line Slope p positive q r undefi ned s negative t Q.. (i C ( +, 7 = T (, _ = C (, = C(, (ii Slope AB = = = (iii Slope p = c(, p: + = ( + = = (iv p: = = + = (v -intercept (, Q.. (a Slope = rise run = = (b -intercept = = + l l l Active Maths (Strands : Ch Solutions

14 (c l (, l + 7 = Active Maths (Strands : Ch Solutions (d l : = ( + l l (7, : = ( 7 +? = 9 +? = (7, l = Q. 7. (i Slope of AB = Slope of BC = (ii B(, C(, k BC ( + ( ( + (k + k k + k k + (iii BC = k k + = k k + = k k = (k + (k = k = OR k = # as k is positive k = (iv AB ( + ( 9 + = Area ABCD = ( = units Q.. (i Slope AB = = = (ii Slope BC = 9 = = m = (( = AB BC (iii = ( = + (iv AB ( + ( + = = = p = (v BC (9 + ( + ( 7 = Area ΔABC = ( ( = ( = units Q. 9. (a BC ( + (9 9 + = 7.7 km (b BE ( + ( 9 + = BE = CE as E is centre of a circle distance from B to E to C = km km 7.7 km =.99 km km. (c Slope AB = =. = = ( = 9 + = is equation of Tangent Street (d Slope = = ( 7 = = is equation of Perpendicular Avenue

15 (e + = + 9 = = + = 7 = = 7 = ( + = + = + = = = (, co-ordinates of museum (f From Town Hall (, to intersection of Straight Road and East Drive (, km Then North on Straight Road to A(,.. km Then travel from A on Tangent Street to Museum (, ( + (. + ( =. km Total distance travelled is = km Q.. (a A(, B(, Slope of AB = = = = m ( Q.. + = ( + = = (b At -ais = = = = C(, (c AB ( + ( ( + ( = = AC ( + ( + 9 = 9 = AB AC = = Slope Line k m l j n Active Maths (Strands : Ch Solutions

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