Question

The points $A(4,-2),B(7,2),C(0,9)$ and $D(-3,5)$ form a parallelogram. Also find the length of the altitude to the base AB.

Answer 1

Given $A(4,-2),B(7,2),C(0,9),D(-3,5)$

The slope of line $AB$ is $\frac{2+2}{7-4}=\frac{4}{3}$

The equation of line $AB$ is

$(y-4)=\frac{4}{3}(x+2)$

$3y-12=4x+8$

$4x-3y+20=0$

The altitude is given by perpendicular from the other vertex

So, Distance from the point $(0,9)$ from $4x-3y+20$ is

$\Rightarrow \frac{|4\left(0\right)-3\left(9\right)+20|}{\sqrt{16+9}}$

$=\frac{|-27+20|}{\sqrt{25}}=\frac{7}{5}$

So the length of Altitude is $\frac{7}{5}$