ICSE Class X Math 2013 Solved Paper

Question : 44

Total: 46

In the figure given below, the line segment AB meets X -axis at A and Y -axis at B . The point P(−3,4) on AB divides it in the ratio 2 : 3. Find the coordinates of A and B.

Solution:

Let the co-ordinates of A and B be (x,0) and (0,y)
∵ The co-ordinates of a point P(−3,4) on AB divides it in the ratio 2:3 .
i.e., AP:PB=2:3
By using section formula,
x‌=‌

m1x2+m2x1

m1+m2

−3‌=‌

2×0+3×x

2+3

⇒‌‌−3‌=‌

⇒3x=−15
x‌=−5
and y‌=‌

m1y2+m2y1

m1+m2

4‌=‌

2×y+3×0

2+3

⇒‌4‌=‌

⇒2y‌=20
⇒y‌=10
Hence, the co-ordinates of A and B are ( -5 , 0) and (0,10). .

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