Question

Which equation set up would we use to find point D if CD is bisected by B at (8,14) and C is located at (-9,-1)

Answer 1

The rule of the midpoint (x, y) of a line that has two endpoints (x1, y1) and (x2, y2) is

`\begin{gathered} x=(x_1+x_2)/(2) \\ y=(y_1+y_2)/(2) \end{gathered}`

Since CD is bisected by B, then

B is the midpoint of CD

Then B = (x, y)

Since B = (8, 14), then

x = 8 and y = 14

Since C = (-9, -1), then

x1 = -9 and y1 = -1

We will use the rule of the midpoint above to find (x2, y2) the coordinates of point D

`8=(-9+x_2)/(2)`

Multiply both sides by 2

`16=-9+x_2`

Add 9 to both sides

`\begin{gathered} 16+9=-9+9+x_2 \\ 25=x_2 \end{gathered}`

The x-coordinate of point D is 25

`14=(-1+y_2)/(2)`

Multiply both sides by 2

`28=-1+y_2`

Add 1 to both sides

`\begin{gathered} 28+1=-1+1+y_2 \\ 29=y_2 \end{gathered}`

The y-coordinate of point D is 29, then

Point D = (25, 29)

We used the equation of the mid-point

`\begin{gathered} x_D=2(x)-x_c \\ y_D=2(y)-y_c \end{gathered}`