Ex 7.2, 8
If A and B are (– 2, – 2) and (2, – 4), respectively, find the coordinates of P such that AP = 3/7 AB & P lies on the line segment AB.
Let the co−ordinates of point P be P(x, y)
It is given that
AP = 3/7 (AB)
AP = 3/7 (AP + PB)
7AP = 3AP + 3PB
7AP − 3AP = 3PB
4AP = 3PB
𝐴𝑃/𝑃𝐵 = 3/4
Hence the point P divides AB in the ratio of 3:4
Finding coordinate of point P
Using section formula
m1 = 3, m2 = 4
x1 = 2, x2 = 2
y1 = −2, y2 = −4
Hence, the co−ordinate of P are P(x, y) = P ((−𝟐)/𝟕 ", " (−𝟐𝟎)/𝟕)
x = (𝑚1 𝑥2 + 𝑚2 𝑥1)/(𝑚1 + 𝑚2)
= (3 × 2 + 4 ×−2)/(3 + 4)
= (6 − 8 )/7
= (−2)/7
y = (𝑚_1 𝑦_2 + 𝑚_2 𝑦_1)/(𝑚_1 + 𝑚_2 )
= (3 ×−4 + 4 ×−2)/(3 + 4)
= (−12 − 8 )/7
= (−20)/7

Davneet Singh has done his B.Tech from Indian Institute of Technology, Kanpur. He has been teaching from the past 13 years. He provides courses for Maths, Science, Social Science, Physics, Chemistry, Computer Science at Teachoo.

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