Question

a rectangle on a coordinate plane has vertices $q(-1,1)$, $r(6,1)$, $s(6,-8)$, and $t(-1,-8)$. what are the dimensions of the rectangle?
the base is 7 and the height is 9.
the base is 9 and the height is 6.
the base is 6 and the height is 9.
the base is 9 and the height is 7.

Explanation:

Step1: Calculate the base length

For two points with the same \(y -\)coordinate (e.g., \(Q(-1,1)\) and \(R(6,1)\)), use the distance formula \(d=\vert x_2 - x_1\vert\).
\(d=\vert6-(-1)\vert=\vert6 + 1\vert=7\)

Step2: Calculate the height length

For two points with the same \(x -\)coordinate (e.g., \(R(6,1)\) and \(S(6,-8)\)), use the distance formula \(d=\vert y_2 - y_1\vert\).
\(d=\vert-8 - 1\vert=\vert-9\vert=9\)

Answer:

The base is \(7\) and the height is \(9\).