Question

Let the line $L$ passes through two given points $P_1\left(x_1,y_1\right)$ and $P_2\left(x_2,y_2\right)$. Let $P(x,y)$ be general point on $L$. Then, the equation of the line passing through the points $\left(x_1,y_1\right)$ and $\left(x_2,y_2\right)$ is given by

• A. $y-y_1=\frac{y_2-y_1}{x_2-x_1}\left(x_1-x\right)$
• B. $y+y_1=\frac{y_1-y_2}{x_1-x_2}\left(x+x_1\right)$
• C. $y-y_1=\frac{y_2-y_1}{x_2-x_1}\left(x-x_1\right)$
• D. $y-y_1=\frac{y_2+y_1}{x_2+x_1}\left(x-x_1\right)$

Answer 1

Answer: (C)

$\because$ The three points $P_1,P_2$ and $P$ are collinear. Therefore, we have
Slope of $P_{1}P=$ Slope of $P_1{P}_2$
i.e., $\frac{\left(y-y_1\right)}{\left(x-x_1\right)}=\frac{\left(y_2-y_1\right)}{\left(x_2-x_1\right)}$
or $(y-y_{1)}=\frac{y_2-y_1}{x_2-x_1}\left(x-x_1\right)$

Thus, Equation of the line passing through the points $\left(x_1,y_1\right)$ and $\left(x_2,y_2\right)$ is given by
$y-y_1=\frac{y_2-y_1}{x_2-x_1}\left(x-x_1\right)$