Question

2.Given that R is the midpoint of segment AX, write an equation if AR = 5x - 15 andRX = 3x + 1. Then find AR, RX, and AX.3.The endpoints of a segment are (-3,4) and (5, -8). Find the length of the segment tothe nearest tenth and then find the coordinates of the midpoint.

Answer 1

2.

Equation: 5x - 15 = 3x + 1

AR: 25

RX: 25

AX: 50

3.

The length of the segment is of 14.4 units.

The coordinates of the midpoint are (1,-2).

Explanation:

2.

Since R is the midpoint of segment AX, we have that:

AR = RX

So

5x - 15 = 3x + 1

5x - 3x = 1 + 15

2x = 16

x = 16/2

x = 8

AR = 5x - 15 = 5*8 - 15 = 40 - 15 = 25

AR = RX = 25

AX = AR + RX = 25 + 25 = 50

3.

To find the length of a segment, we find the distance between their endpoints. The distance between points (x1,y1) and (x2,y2) is given by:

`D=\sqrt[]{(x2-x1)^2+(y2-y1)^2}`

The midpoint of a segment is the mean of the coordinates of their endpoints.

Length of the segment:

Segment between points (-3,4) and (5,-8). So

`D=\sqrt[]{(5-(-3))^2+(-8-4)^2}=\sqrt[]{8^2+12^2}=\sqrt[]{208}=14.4`

The length of the segment is of 14.4 units.

Coordinates of the midpoint:

Midpoint of (-3,4) and (5,-8).

x-coordinate:

(-3+5)/2 = 2/2 = 1

y-coordinate:

(4-8)/2 = -4/2 = -2

The coordinates of the midpoint are (1,-2).