Question

1. part a alice plotted the entry court on graph paper. find the midpoint of cd. if you construct a line perpendicular to the angle bisector through point e. does the perpendicular line pass through point b? part b is the midpoint of be on the angle bisector? explain your reasoning

Explanation:

Step1: Find coordinates of points C and D

From the graph, assume each grid is 1 unit. Let \(C(- 4,5)\) and \(D(1,5)\)

Step2: Use mid - point formula

The mid - point formula for two points \((x_1,y_1)\) and \((x_2,y_2)\) is \(M(\frac{x_1 + x_2}{2},\frac{y_1 + y_2}{2})\)
Substitute \(x_1=-4,y_1 = 5,x_2 = 1,y_2=5\) into the formula:
\(x=\frac{-4 + 1}{2}=\frac{-3}{2}=-1.5\), \(y=\frac{5 + 5}{2}=5\)

Answer:

The mid - point of \(\overline{CD}\) is \((-1.5,5)\)