ICSE Class X Math 2016 Solved Paper

A line AB meets X-axis at A and Y-axis at B.P(4,−1) divides AB in the ratio 1:2.

Question : 37

Total: 57

Find the equation of the line through P and perpendicular to AB.

Solution:

Slope of AB(m)‌=‌

y2−y1

x2−x1

‌=‌

−3−0

0−6

=‌

−3

−6

=‌

Slop of perpendicular bisector of AB
m2=−‌

=−‌

1∕2

=−2
Equation of required line
y−y1‌=m(x−x1)
‌y−(−1)‌=−2(x−4)
⇒y+1‌=−2x+8
⇒2x+y=7‌

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