Question

1. how do you find the vertices of a regular polygon inscribed in a circle?

a. by calculating the perimeter of the polygon.
b. by measuring the angles with a ruler.
c. by drawing tangents to the circle.
d. by dividing the circle into equal arcs using the central angles.

1. what is the length of a line segment between points (2, -2) and (-5, 6)?

a. 6.3 units
b. 4 units
c. 12 units
d. 10.6 units

Explanation:

3.

To find the vertices of a regular polygon inscribed in a circle, we divide the circle into equal - arcs using central angles. The central angles are calculated as $\frac{360^{\circ}}{n}$ where $n$ is the number of sides of the polygon. Each vertex of the polygon lies at the intersection of the circle and the rays forming these central angles. Calculating the perimeter doesn't help in finding vertices directly. A ruler is used for measuring lengths, not angles. Drawing tangents is not related to finding the vertices of an inscribed polygon.

Step1: Recall the distance formula

The distance $d$ between two points $(x_1,y_1)$ and $(x_2,y_2)$ is given by $d = \sqrt{(x_2 - x_1)^2+(y_2 - y_1)^2}$. Here, $x_1 = 2,y_1=-2,x_2=-5,y_2 = 6$.

Step2: Substitute the values

$d=\sqrt{(-5 - 2)^2+(6+2)^2}=\sqrt{(-7)^2+8^2}=\sqrt{49 + 64}=\sqrt{113}\approx10.6$

Answer:

d. By dividing the circle into equal arcs using the central angles.

4.