Question

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

Answer 1

Answer:

$D = (-4,-9)$

Step-by-step 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:

$M(x,y) = \frac{1}{2}(x_1 + x_2, y_1 + y_2)$

So, we have:

$(-1,-1) = \frac{1}{2}(2 + x_2, 7 + y_2)$

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:

$D = (x_2,y_2)$

$D = (-4,-9)$