Question

The line joining the points $(-1,3)$and $(4,-2)$ will pass through the point $(p,q)$if

• A. $p–q=1$
• B. $p+q=1$
• C. $p–q=2$
• D. $p+q=2$

Answer 1

The correct option is D

$p+q=2$

Explanation for the correct option

Since a line joining the points $(-1,3)$and $(4,-2)$ will pass through the point $(p,q)$

Then, all three points are collinear points

The slope of the line joining $(-1,3)$and $(4,-2)$ = The slope of the line joining $(4,-2)$ and $(p,q)$

$\Rightarrow \frac{y_2-y_1}{x_2-x_1}=\frac{y_3-y_2}{x_3-x_2}$ [ Two point form of the slope]

$\Rightarrow \frac{-2-\left(3\right)}{4-\left(-1\right)}=\frac{q-\left(-2\right)}{p-4}$

$$\begin{gathered} \Rightarrow \frac{-5}{5}=\frac{q+2}{p-4} \\ \Rightarrow -1=\frac{q+2}{p-4} \\ \Rightarrow \left(-p\right)+4=q+2 \\ \Rightarrow p+q=4 \end{gathered}$$

Hence, Option $\left(\mathrm{D}\right)$ is correct.