Question

Part A: Plot the points A(-8,7) and B(6,-9). Mark the halfway point on AB and label it point M. What are the coordinates of M? Part B: Plot point C(2,7). If M is the midpoint of CD, what are the coordinates of D?

please help me

Answer 1

a.
`M(x,y) = (-1,-1)`

b.
`D(-4,-9)`

Explanation:

Given

A(-8,7) and B(6,-9).

Solving (a):

Determine the Midpoint M;

This is calculated as follows;

`M(x,y) = ((x_1+x_2)/(2),(y_1+y_2)/(2))`

Where

`(x_1,y_1) = (-8,7)`

`(x_2,y_2) = (6,-9)`

Substitute these values in the formula

`M(x,y) = ((-8+6)/(2),(7-9)/(2))`

`M(x,y) = ((-2)/(2),(-2)/(2))`

`M(x,y) = (-1,-1)`

Hence; the midpoint is (-1,-1)

Solving (a):

Here, we have

C = (2,7)

M; Midpoint = (-1,-1)

Required: Determine D

This is calculated as follows;

`M(x,y) = ((x_1+x_2)/(2),(y_1+y_2)/(2))`

Where

`(x_1,y_1) = (2,7)`

`(x,y) = (-1,-1)`

Substitute these values in the formula

`(-1,-1) = ((2+x_2)/(2),(7+y_2)/(2))`

Solving for x2

`-1 = (2 + x_2)/(2)`

Multiply both sides by 2

`-2 = 2 + x_2`

Subtract 2 from both sides

`x_2 = -2 - 2`

`x_2 = -4`

Solving for y2

`-1 = (7 + y_2)/(2)`

Multiply both sides by 2

`-2 = 7 + y_2`

Subtract 7 from both sides

`y_2 = -2 - 7`

`y_2 = -9`

Hence, the coordinates of D is

`D(-4,-9)`