Question

on the coordinate plane, the segment from x(-2, 2) to y(8, 2) forms one side of △xyz. the triangle has an area of 20 square units. select all of the points where z could be.
(0, 6)
(7, -2)
(4, 2)
(8, 6)

Explanation:

Step1: Calculate the length of side XY

The distance formula for 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 $X(-2,2)$ and $Y(8,2)$, since $y_1 = y_2=2$, the length of $XY$ is $|8-(-2)|=10$.

Step2: Use the triangle - area formula

The area formula of a triangle is $A=\frac{1}{2}\times base\times height$. Given $A = 20$ and base $b = XY=10$, we substitute into the formula $20=\frac{1}{2}\times10\times h$. Solving for $h$ gives $h = 4$.

Step3: Check the distance of each point from the line $y = 2$

The line containing segment $XY$ is $y = 2$.

• For point $(0,6)$: The distance from the line $y = 2$ is $|6 - 2|=4$.
• For point $(7,-2)$: The distance from the line $y = 2$ is $| - 2-2|=4$.
• For point $(4,2)$: The distance from the line $y = 2$ is $|2 - 2|=0$.
• For point $(8,6)$: The distance from the line $y = 2$ is $|6 - 2|=4$.

Answer:

$(0,6),(7,-2),(8,6)$