Question

1. what is the distance between points (4,3) and (7,7)?

a. 4 units
b. 2 units
c. 5 units
d. 6 units

1. what are the properties of a bisected angle?

a. it changes the angle size
b. the angle becomes obtuse
c. the angle is divided into two equal parts
d. each segment is congruent

Explanation:

Step1: Recall distance formula

The distance formula between two points $(x_1,y_1)$ and $(x_2,y_2)$ is $d = \sqrt{(x_2 - x_1)^2+(y_2 - y_1)^2}$. Here, $(x_1,y_1)=(4,3)$ and $(x_2,y_2)=(7,7)$.

Step2: Substitute values

$d=\sqrt{(7 - 4)^2+(7 - 3)^2}=\sqrt{3^2+4^2}=\sqrt{9 + 16}=\sqrt{25}=5$.

For the second - question:
The definition of an angle bisector is a ray that divides an angle into two equal parts.

Answer:

1. C. 5 units
2. C. The angle is divided into two equal parts