Answer:
Point Q is at (6, 6).
Step-by-step 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:
[tex]\displaystyle M=\Big(\frac{x_1+x_2}{2},\frac{y_1+y_2}{2}\Big)[/tex]
We will let R(10, 10) be (x₁, y₁). We are also given that M is at (8, 8). Therefore:
[tex]\displaystyle (8, 8)=\Big(\frac{10+x}{2}, \frac{10+y}{2}\Big)[/tex]
This gives us two cases:
[tex]\displaystyle \frac{10+x}{2}=8\text{ and } \frac{10+y}{2}=8[/tex]
Solve for each case. Multiply both sides by 2:
[tex]10+x=16\text{ and } 10+y=16[/tex]
And we can subtract 10 from both sides:
[tex]x=6\text{ and } y=6[/tex]
Therefore, Point Q is at (6, 6).
