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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.​

2 Answers

2 votes

Answer:

Point Q: ( 6, 6)

Explanation:

(10, 10)

- 2 (8, 8)

( 6, 6)

User Arnaud Tournier
by
8.2k points
3 votes

Answer:

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).

User Meherzad
by
8.7k points

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