Question

Area of the triangle formed by the lines $7x-2y+10=0,7x+2y-10=0,y+2=0$ is

• A. $7$
• B. $14$
• C. $18$
• D. $12$

Answer 1

The correct option is B $14$

$7x-2y+10=0$ ---(1)

$7x+2y-10=0$ ---(2)

$y=-2$ ---(3)

Add 1 & 2,

$7x=0$

$x=0$ & $y=5$

From 1 & 3,

$y=-2,x=-2$

From 2 & 3,

$y=-2,x=2$

So, triangle ABC

$\therefore$ area of $\Delta ABC=\frac{1}{2}\left[x_1\right(y_2-y_3)+x_2(y_3-y_1)+x_3(y_1-y_2\left)\right]$

$=\frac{1}{2}\left[0\right(-2+2)+(-2\left)\right(-7)+2(7\left)\right]$

$=\frac{28}{2}=14$ sq. units