Question

rectangle
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plot the vertices $(-2,-8),(-2,2)$, and $(8,2)$.
what is the last vertex of the rectangle?
what is the area of the rectangle?
square units

Explanation:

Step1: Find the last vertex

In a rectangle, opposite sides are equal and parallel.
The \(x -\)coordinate of the fourth vertex: Since the \(x -\)coordinate of the first two points is \(-2\) and for the third point is \(8\). The fourth point's \(x -\)coordinate should be \(8\) (to be parallel to the side connecting \((-2,-8)\) and \((-2,2)\)).
The \(y -\)coordinate of the fourth vertex: Since the \(y -\)coordinate of the second and third points is \(2\) and for the first point is \(-8\). The fourth point's \(y -\)coordinate should be \(-8\) (to be parallel to the side connecting \((-2,2)\) and \((8,2)\)).
So the last vertex is \((8,-8)\).

Step2: Calculate the length and width

The length of the vertical side (using the \(y -\)coordinates of \((-2,-8)\) and \((-2,2)\)): \(l=\vert2 - (-8)\vert=\vert2 + 8\vert = 10\)
The length of the horizontal side (using the \(x -\)coordinates of \((-2,2)\) and \((8,2)\)): \(w=\vert8-(-2)\vert=\vert8 + 2\vert=10\)

Step3: Calculate the area

The area of a rectangle \(A = l\times w\)
Substitute \(l = 10\) and \(w = 10\) into the formula: \(A=10\times10 = 100\)

Answer:

The last vertex is \((8,-8)\) and the area is \(100\) square units.