Question

using the figure below, find the area of the rectangle on the coordinate plane. what is the distance between points a and b? multiple - choice question a(0,0) b(4, - 4) c(7, - 1) d(3,3) dab = \sqrt{(0 - 4)^2+(0 + 4)^2}=\sqrt{16 + 16}=\sqrt{32}=4\sqrt{2}\approx5.7 units dad = \sqrt{(0 - 3)^2+(0 - 3)^2}=\sqrt{9 + 9}=\sqrt{18}=3\sqrt{2}\approx4.2 units

Explanation:

Step1: Recall distance formula

The distance formula between two points $(x_1,y_1)$ and $(x_2,y_2)$ is $d = \sqrt{(x_2 - x_1)^2+(y_2 - y_1)^2}$. For points $A(0,0)$ and $B(4, - 4)$, $x_1 = 0,y_1 = 0,x_2 = 4,y_2=-4$.

Step2: Substitute values

$d=\sqrt{(4 - 0)^2+(-4 - 0)^2}=\sqrt{16 + 16}=\sqrt{32}=4\sqrt{2}\approx5.7$ units.

Answer:

5.7 units