ICSE Class X Math 2015 Solved Paper

In the given figure ABC is a triangle and BC is parallel to the y-axis. AB and AC intersects the y-axis at P and Q respectively.

Question : 26

Total: 52

Find the ratio in which Q divides AC.

Solution:

Let the ratio be k:1
∴ Coordinates of P is
(‌

m1x2+m2x1

m1+m2

,‌

m1y2+m2y1

m1+m2

) =(‌

−2k+y

k+1

,‌

−4k

k+1

)
Let coordinates of P is (x,y) .
x‌=‌

−2k+4

k+1

0‌=‌

−2k+4

k+1

‌‌‌ [as P lies on ‌y‌-axis] ‌
2k‌=4⇒k=2
‌ Ratio ‌‌=2:1

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