Question

What is the area of the rectangle?

Answer 1

We have been given a graph having coordinate of 4 points which are : (-2,8), (4,9), (6,-3) and (0,-4).

Question says that they are corner points of the rectangle so we can apply distance formula

$d=\sqrt{\left(x_2-x_1\right)^2+\left(y_2-y_1\right)^2}$

to find the lenght and width of that rectangle.

$AB=\sqrt{\left(4--2\right)^2+\left(9-8\right)^2}$

$AB=\sqrt{\left(4+2\right)^2+\left(9-8\right)^2}$

$AB=\sqrt{6^2+1^2}$

$AB=\sqrt{36+1}$

$AB=\sqrt{37}$

$BC=\sqrt{\left(4-6\right)^2+\left(9--3\right)^2}$

$BC=\sqrt{\left(4-6\right)^2+\left(9+3\right)^2}$

$BC=\sqrt{\left(-2\right)^2+12^2}$

$BC=\sqrt{4+144}$

$BC=\sqrt{148}$

$BC=2\sqrt{37}$

Now to find the area we will multiply length (AB) and width (BC)

Area of the rectangle $=\sqrt{37}\cdot2\sqrt{37}$

Area of the rectangle =2*37=74

Hence final answer is 74 square units.