Mathematics: If Q is the midpoint of PR, find the coordinates of R if P(11,-2) and Q(4,3).

It is so I had to look it up on here lol I’m so sry it is the right answer i swear...

If Q is the midpoint of PR, find the coordinates

lillianmitchell580

01.08.2021

R = (-3, 8).

Step-by-step explanation:

Recall the midpoint formula:

$\displaystyle M=\left(\frac{x_1+x_2}{2}, \frac{y_1+y_2}{2}\right)$

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:

$\displaystyle (4, 3)=\left(\frac{11+x_2}{2}, \frac{-2+y_2}{2}\right)$

Split into two separate equations:

$\displaystyle \frac{11+x_2}{2}=4\text{ and } \frac{-2+y_2}{2}=3$

Solve for each case:

$\displaystyle 11+x_2=8\Rightarrow x_2=-3$

$\displaystyle -2+y_2=6\Rightarrow y_2=8$

Therefore, our second point (x₂, y₂) is (-3, 8).

Hence, R = (-3, 8).

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