Question

in the standard (x,y) coordinate plane below, the points (-5,0), (5,0), (9,5), and (-1,5) are vertices of a parallelogram. what is the area, in square coordinate units, of the parallelogram? 25 50 80√2 110√2

Explanation:

Step1: Calculate the base length

The base of the parallelogram can be found using the distance formula for two points on the \(x -\)axis. For points \((- 5,0)\) and \((5,0)\), the distance \(b=\vert x_2 - x_1\vert\). Here, \(x_1=-5\), \(x_2 = 5\), so \(b=\vert5-(-5)\vert=10\).

Step2: Calculate the height

The height \(h\) of the parallelogram is the vertical distance between the two parallel sides. The \(y -\)coordinate of the upper - side is \(y = 5\) and the \(y -\)coordinate of the lower - side is \(y = 0\). So \(h=\vert5 - 0\vert=5\).

Step3: Calculate the area of the parallelogram

The area formula of a parallelogram is \(A=b\times h\). Substitute \(b = 10\) and \(h = 5\) into the formula, we get \(A=10\times5=50\).

Answer:

\(50\)