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Question

Find the ratio in which the point P(1, 2) divides the line joining the points A(-2, 1) and B(7, 4).

A
1:2
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B
2:3
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C
3:4
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D
1:3
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Solution

The correct option is A 1:2
Plotting the given points on graph paper we get:

By subtracting the cooresponding corrdinates we get:
AX = 1 - ( - 2) = 3
PX = 2 - 1 = 1

AY = 7 - (-2) = 9
BY = 4 - 1 = 3

We know that trinagle APX is similar to triangle ABY by AA rule.
APAB=AXAY

APAB=39

APAB=13

APAP+PB=13

Reducing the above equation we get:
APPB=12

The ratio in which 'P' divides AB is 1 : 2

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