Question

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

Answer 1

(15/2),(1/2)

Explanation:

(x1 + x2 / 2) , (y1 + y2) / 2)

(11 + 4 / 2) , (-2 + 3 / 2)

(15/2) , (1/2)

Answer 2

R = (-3, 8).

Explanation:

Recall the midpoint formula:

`\displaystyle M=\left((x_1+x_2)/(2), (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((11+x_2)/(2), (-2+y_2)/(2)\right)`

Split into two separate equations:

`\displaystyle (11+x_2)/(2)=4\text{ and } (-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).