Question

The equation of one side of a rectangle is $3x-4y-10=0$ and the coordinates of two of its vertices are $(-2,1)$ and $(2,4)$. Then, the area of the rectangle is

• A. $20$ sq.units
• B. $40$ sq.units
• C. $10$ sq.units
• D. $30$ sq.units

Answer 1

Answer: (A)

$20$ sq.units

Given equation of side of rectangle
$3x-4y-10=0$
Points $(-2,1)$ and $(2,4)$ do not lie on the line .
Slope of this line is $\frac{3}{4}$
So, the slope of other side (perpendicular side) is $-\frac{4}{3}$
Equation of side passing through $(2,4)$ and slope $-\frac{4}{3}$ is
$y-4=-\frac{4}{3}(x-2)$
$4x+3y=20$
Now, length of perpendicular from $(-2,1)$ on line $3x-4y-10=0$ is
$p_1=\frac{|-20|}{5}=4$
Length of perpendicular from $(-2,1)$ on line $4x+3y-20=0$ is
$p_2=\frac{|-25|}{5}=5$

Area of rectangle $=p_1\times p_2=20$ sq.units