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發問:
Find the coordinates of the points P,Q which divide internally and externally in the ratio 2:3 the line joining the points A (8,10), B (18,20) , and show that MP.MQ =MB.MB where M is the midpoint of AB.
最佳解答:
Find the coordinates of the points P,Q which divide internally and externally in the ratio 2:3 the line joining the points A (8,10), B (18,20) , and show that MP.MQ =MB.MB where M is the midpoint of AB. Let P (x1, y1) divides A and B internally Let Q (x2, y2) divides A and B externally P(x1, y1) = (8 + (18-8) * 2 / (2+3), 10 + (20-10) * 2 / (2+3)) 【As P is a point between A and B with AP/PB = 2/3】 P(x1, y1) = (12, 14) Q(x2, y2) = (18 - 3(18-8), 20 - 3(20-10)) 【As Q is a point left to A with QB = 3AB】 Q(x2, y2) = (-12, -10) Let M(x3, y3) be the mid-point of A and B M(x3, y3) = ((18+8)/2, (20+10)/2) M(x3, y3) = (13, 15) MP = √[(13-12)2 + (15-14)2] MP = √[12 + 12] MP = √2 .............. (1) MQ = √[(13 - (-12))2 + (15 - (-10))2] MQ = √[252 + 252] MQ = √1250 ............. (2) MB = √[(18-13)2 + (20-15)2] MB = √[52 + 52] MB = √50 .............. (3) MP.MQ = √2 + √1250 【From (1), (2)】 MP.MQ = √(2*1250) MP.MQ = √(2500) MP.MQ = √50√50 MP.MQ = MB.MB 【From (3)】 So MP.MQ = MB.MB
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Straight line -----A.Maths''發問:
Find the coordinates of the points P,Q which divide internally and externally in the ratio 2:3 the line joining the points A (8,10), B (18,20) , and show that MP.MQ =MB.MB where M is the midpoint of AB.
最佳解答:
Find the coordinates of the points P,Q which divide internally and externally in the ratio 2:3 the line joining the points A (8,10), B (18,20) , and show that MP.MQ =MB.MB where M is the midpoint of AB. Let P (x1, y1) divides A and B internally Let Q (x2, y2) divides A and B externally P(x1, y1) = (8 + (18-8) * 2 / (2+3), 10 + (20-10) * 2 / (2+3)) 【As P is a point between A and B with AP/PB = 2/3】 P(x1, y1) = (12, 14) Q(x2, y2) = (18 - 3(18-8), 20 - 3(20-10)) 【As Q is a point left to A with QB = 3AB】 Q(x2, y2) = (-12, -10) Let M(x3, y3) be the mid-point of A and B M(x3, y3) = ((18+8)/2, (20+10)/2) M(x3, y3) = (13, 15) MP = √[(13-12)2 + (15-14)2] MP = √[12 + 12] MP = √2 .............. (1) MQ = √[(13 - (-12))2 + (15 - (-10))2] MQ = √[252 + 252] MQ = √1250 ............. (2) MB = √[(18-13)2 + (20-15)2] MB = √[52 + 52] MB = √50 .............. (3) MP.MQ = √2 + √1250 【From (1), (2)】 MP.MQ = √(2*1250) MP.MQ = √(2500) MP.MQ = √50√50 MP.MQ = MB.MB 【From (3)】 So MP.MQ = MB.MB
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