Question

QR has a midpoint at M(8,8). Point R is at (10, 10). Find the coordinates of point Q. Write the coordinates as decimals or integers.​

Answer 1

Point Q: ( 6, 6)

Explanation:

(10, 10)

- 2 (8, 8)

( 6, 6)

Answer 2

Point Q is at (6, 6).

Explanation:

Segment QR has a midpoint M at (8, 8).

Point R is at (10, 10), and we want to determine the location of Point Q.

First, recall that the midpoint is given by the formula:

`\displaystyle M=\Big((x_1+x_2)/(2),(y_1+y_2)/(2)\Big)`

We will let R(10, 10) be (x₁, y₁). We are also given that M is at (8, 8). Therefore:

`\displaystyle (8, 8)=\Big((10+x)/(2), (10+y)/(2)\Big)`

This gives us two cases:

`\displaystyle (10+x)/(2)=8\text{ and } (10+y)/(2)=8`

Solve for each case. Multiply both sides by 2:

`10+x=16\text{ and } 10+y=16`

And we can subtract 10 from both sides:

`x=6\text{ and } y=6`

Therefore, Point Q is at (6, 6).