Question

find the length of side cd for the quadrilateral shown.

Explanation:

Step1: Identify coordinates of C and D

Let \(C=(5,7)\) and \(D=(5,1)\)

Step2: Apply distance formula for points with same x - coordinate

The distance \(d\) between two points \((x_1,y_1)\) and \((x_2,y_2)\) is \(d = \sqrt{(x_2 - x_1)^2+(y_2 - y_1)^2}\). Since \(x_1=x_2 = 5\), the formula simplifies to \(d=\vert y_2 - y_1\vert\). Here \(y_1 = 7\) and \(y_2=1\), so \(d=\vert7 - 1\vert\)

Step3: Calculate the distance

\(d=\vert7 - 1\vert=6\)

Answer:

6