Question

The distance of the point $(2,3)$ from the line $2x-3y+9=0$ measured along a line $x-y+1=0$ is

• A. $\sqrt{2}$
• B. $4\sqrt{2}$
• C. $2\sqrt{2}$
• D. $3\sqrt{2}$

Answer 1

The correct option is C $2\sqrt{2}$

Consider the following equation.

$2x-3y+9=0$

$x-y+1=0$

$p=(2,3)$

$2x-2y=-2$

$2x-3y=-9$

$x=(6,7)$

Using a distance formula. And calculate x $ y value we get.

$d=\sqrt{{(x_2-x_{\$1})}^2+{(y_2-y_1)}^2}$

$=\sqrt{{(6-2)}^2+{(7-3)}^2}$

$=2\sqrt{2}$

Hence, this is the required answer.