Question

a rectangle on a coordinate plane has vertices ( l(0,6) ), ( m(8,6) ), ( n(8,0) ), and ( o(0,0) ). what are the dimensions of the rectangle? the base is 8 and the height is 8. the base is 6 and the height is 6. the base is 8 and the height is 6. the base is 6 and the height is 8.

Explanation:

Step1: Calculate the length of the base

For points \(L(0,6)\) and \(M(8,6)\), since the \(y -\)coordinates are the same (\(y = 6\)), we use the distance formula for points \((x_1,y_1)\) and \((x_2,y_2)\) on a horizontal line \(d=\vert x_2 - x_1\vert\).
\(d_{LM}=\vert8 - 0\vert=8\)

Step2: Calculate the length of the height

For points \(M(8,6)\) and \(N(8,0)\), since the \(x -\)coordinates are the same (\(x = 8\)), we use the distance formula for points \((x_1,y_1)\) and \((x_2,y_2)\) on a vertical line \(d=\vert y_2 - y_1\vert\).
\(d_{MN}=\vert0 - 6\vert=6\)

Answer:

The base is \(8\) and the height is \(6\).