Question

what are the dimensions of the rectangle shown on the coordinate plane? the base is 9 units and the height is 4 units. the base is 10 units and the height is 4 units. the base is 3 units and the height is 9 units. the base is 11 units and the height is 6 units.

Explanation:

Step1: Calculate the base length

The base of the rectangle is along the x - axis. If we consider two points on the base (for example, \(Z(1,-5)\) and \(Y(10,-5)\)). Using the distance formula for points on a horizontal line (\(y = y_1=y_2\)), the distance \(d=\vert x_2 - x_1\vert\). Here \(x_1 = 1\), \(x_2=10\), so \(d=\vert10 - 1\vert=9\) units.

Step2: Calculate the height

The height of the rectangle is along the vertical line. If we consider two points \(W(1,-1)\) and \(Z(1,-5)\). Using the distance formula for points on a vertical line (\(x = x_1=x_2\)), the distance \(d=\vert y_2 - y_1\vert\). Here \(y_1=-1\), \(y_2 = - 5\), so \(d=\vert-5+1\vert = 4\) units.

Answer:

The base is 9 units and the height is 4 units.