Let and be two vertices of a triangle

MATHEMATICS · Multi-part · CBSE · Mathematics · Coordinate Geometry · Coordinate Geometry

Problem

Let

A(2,-3)

and

B(6,5)

be two vertices of a triangle

ABC

. The point

C(x,y)

satisfies the following conditions: (i) Obtain the coordinates of the midpoint of

AC

in terms of

x

and

y

, and hence write down the first equation relating

x

and

y

. (ii) Using condition (b), derive the second equation relating

x

and

y

. (iii) Solve the simultaneous equations to find the coordinates of

C

. (iv) Verify that the midpoint found in part (i) indeed satisfies the given line equation.