NIMCET 2015 — Mathematics PYQ

In any triangle, the line segment joining the midpoints of two sides is parallel to the third side and half its length.

• Let $D(2,1)$ be the midpoint of $BC$.

• Let $E(-1,-2)$ be the midpoint of $CA$.

• Let $F(3,3)$ be the midpoint of $AB$.

The side $BC$ is parallel to the segment $EF$ (the line joining the midpoints of the other two sides).

2. Find the Slope of side $BC$

Since $BC\parallel EF$, the slope of $BC$ ($m_{BC}$) is equal to the slope of $EF$.

Using the slope formula $m=\frac{y_2-y_1}{x_2-x_1}$ for points $E(-1,-2)$ and $F(3,3)$:

Therefore, $m_{BC}=\frac{5}{4}$.

3. Find the Equation of line $BC$

The line $BC$ passes through its midpoint $D(2,1)$ and has a slope of $\frac{5}{4}$. Using the point-slope form $y-y_1=m(x-x_1)$:

Multiply the entire equation by $4$:

Rearrange into general form $ax+by+c=0$:

Correct Option: (b)