If $A (5, 2), B (3, 4), C (x, y)$ are collinear and $A B = B C$ then find $(x, y)$ .

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Solution

Given $A, B, C$ are collinear and $A B = B C$

So, $B$ is the midpoint of the line segment $A C$ .

by using midpoint formula

$x = (\frac{x_{1} + x_{2}}{2}) a n d y = (\frac{y_{1} + y_{2}}{2})$

So $\frac{5 + x}{2} = 3$
$5 + x = 6$
$x = 1$

Also, $\frac{2 + y}{2} = 4$
$2 + y = 8$
$y = 6$

Hence, $C (x, y)$ is $C (1, 6)$ .

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