Answer:
R = (-3, 8).
Step-by-step explanation:
Recall the midpoint formula:
[tex]\displaystyle M=\left(\frac{x_1+x_2}{2}, \frac{y_1+y_2}{2}\right)[/tex]
Where M is the midpoint, (x₁, y₁) is one point and (x₂, y₂) is another.
We are given that Q is the midpoint of PR, where P = (11, -2) and Q = (4, 3) and we want to find the coordinates of R.
Substitute Q for M and let P(11, -2) be (x₁, y₁). Hence:
[tex]\displaystyle (4, 3)=\left(\frac{11+x_2}{2}, \frac{-2+y_2}{2}\right)[/tex]
Split into two separate equations:
[tex]\displaystyle \frac{11+x_2}{2}=4\text{ and } \frac{-2+y_2}{2}=3[/tex]
Solve for each case:
[tex]\displaystyle 11+x_2=8\Rightarrow x_2=-3[/tex]
[tex]\displaystyle -2+y_2=6\Rightarrow y_2=8[/tex]
Therefore, our second point (x₂, y₂) is (-3, 8).
Hence, R = (-3, 8).
