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)

Explanation:

Step1: Recall distance formula

$d = \sqrt{(x_2 - x_1)^2+(y_2 - y_1)^2}$
For points $A(0,0)$ and $B(4, - 4)$:
$d_{AB}=\sqrt{(4 - 0)^2+(-4 - 0)^2}=\sqrt{16 + 16}=\sqrt{32}=4\sqrt{2}\approx5.7$

Step2: For points $A(0,0)$ and $D(3,3)$

$d_{AD}=\sqrt{(3 - 0)^2+(3 - 0)^2}=\sqrt{9+9}=\sqrt{18}=3\sqrt{2}$
Area of rectangle $A = d_{AB}\times d_{AD}=\sqrt{32}\times\sqrt{18}=\sqrt{32\times18}=\sqrt{576}=24$

Answer:

24 square units