Question

If the middle points of the sides $BC,CA$ and $AB$ of the triangle $ABC$ be $(1,3),(5,7)$ and $(-5,7)$respectively then the equation of the side $AB$ is

• A. $x-y-2=0$
• B. $x-y+12=0$
• C. $x+y-12=0$
• D. None of these.

Answer 1

The correct option is B

$x-y+12=0$

Explanation of the correct option.

Find the required equation.

Given : The middle points of the sides $BC,CA$ and $AB$ of the triangle $ABC$ are $(1,3),(5,7)$ and $(-5,7)$respectively.

From the figure we can see that $AB$ is parallel to the line joining midpoints of $AC$ and $BC$.

Therefore, the slope of $AB=$slope of line joining midpoints of $AC$ and $BC$

Thus, slope of $AB=\frac{y_2-y_1}{x_2-x_1}$

slope of $AB=\frac{7-3}{5-1}$

slope of $AB=1$

Therefore the equation of $AB$,

$\begin{array}{rcl}y-7& =& 1(x+5)\\ & \Rightarrow & x-y+12=0\end{array}$

Hence option $\left(B\right)$ is the correct option.