Question

What is the area of the rectangle? 60 units² 66 units² 70 units² 74 units² A rectangle is graphed on a coordinate plane. The horizontal x-axis ranges from negative 10 to 10 in increments of 1. The vertical y-axis ranges from negative 10 to 10 in increments of 1. The vertices of the rectangle lie on begin ordered pair negative 2 comma 8 end ordered pair and begin ordered pair 4 comma 9 end ordered pair and begin ordered pair 6 comma negative 3 end ordered pair and begin ordered pair 0 comma negative 4 end ordered pair.

Answer 1

74 units squared

Explanation:

Answer 2

Given vertices of the rectangle :

(-2,8)

(4,9)

(6,-3) and (0,-4)

Length of the rectangle is the distance of (-2,8) to (4,9).

`\mathrm{Compute\:the\:distance\:between\:}\left(x_1,\:y_1\right),\:\left(x_2,\:y_2\right):\quad √(\left(x_2-x_1\right)^2+\left(y_2-y_1\right)^2)`

`=√(\left(4-\left(-2\right)\right)^2+\left(9-8\right)^2)`

`=√(37)`

Width of the rectangle is the distance of (4,9) and (6,-3).

`=√(\left(6-4\right)^2+\left(-3-9\right)^2)`

`=2√(37)`

Area of the rectangle = Length × Width

=
`√(37)* 2√(37)`

= 2 × 37

= 74.

Therefore, area of the rectangle is 74 units².