Answer:
See attachment for diagram
Step-by-step explanation:
Given
[tex](x_1,y_1) = (-8,8)[/tex]
[tex](x_2,y_2) = (-3,8)[/tex]
[tex]Area = 15[/tex]
Required
Draw the rectangle on a coordinate plane --- (missing from the question)
First, we calculate the distance between the given pairs.
[tex]D = \sqrt{(x_1 - x_2)^2 + (y_1-y_2)^2}[/tex]
[tex]D = \sqrt{(-8-(-3))^2 + (8-8)^2}[/tex]
[tex]D = \sqrt{25}[/tex]
[tex]D = 5[/tex]
So, the distance between the given pairs is 5 units... Let this be the length of the rectangle.
Using:
[tex]Area = Length * Width[/tex]
[tex]15 = 5 * Width[/tex]
[tex]Width = \frac{15}{5}[/tex]
[tex]Width = 3[/tex]
The width is 3 units.
This implies that the opposite sides of the rectangle are either 3 units down or 3 units up the given pairs.
Assume they are 3 units up.
[tex](x_1,y_1) = (-8,8)[/tex] and [tex](x_2,y_2) = (-3,8)[/tex]
[tex](x_3,y_3) = (x_1,y_3 + 3) = (-8,8+3) = (-8,11)[/tex]
[tex](x_4,y_4) = (x_2,y_2 + 3) = (-3,8+3) = (-3,11)[/tex]
