Question

Part B: Plot point C(2,7). If M is the midpoint of CD, what are the coordinates of D?

Answer 1

`D = (-4,-9)`

Explanation:

Given

`C =(2,7)`

`M=(-1,-1)`

Required

The coordinates of D

Represent D with:

`D = (x_2,y_2)`

Using midpoint formula, we have:

`M(x,y) = (1)/(2)(x_1 + x_2, y_1 + y_2)`

So, we have:

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

Multiply both sides by 2

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

Compare both sides

`2 + x_2 = -2`

`7 + y_2 =-2`

In
`2 + x_2 = -2`, we have:

`x_2 =-2-2`

`x_2 =-4`

In
`7 + y_2 =-2`, we have:

`y_2 = -2 - 7`

`y_2 = -9`

So, the coordinates of D is:

`D = (x_2,y_2)`

`D = (-4,-9)`