Question

Line QR has a midpoint at M (5, 5). Point Q is at (9, 1). Find the coordinates of point R.

Answer 1

R (1, 9)

Explanation:

Pre-Solving

We are given that QR has a midpoint, M which is at the point (5,5). We also know that Q is (9, 1).

We want to find the coordinates of R.

Recall that the midpoint formula is
`((x_1+x_2)/(2), (y_1+y_2)/(2) )`, where
`(x_1, y_1)` and
`(x_2,y_2)` are points.

Since we know that (5,5) is the midpoint, this means that
`(x_1+x_2)/(2) = 5` and
`(y_1+y_2)/(2) = 5`. We can also label the values of Q as
`x_1` and
`y_1` respectively, so point R is the coordinate
`(x_2, y_2)`.

So that means:

`(9+x_2)/(2) = 5`

`(1+y_2)/(2) = 5`

Solving

We can solve these equations to find the values of
`(x_2,y_2)`.

`(9+x_2)/(2) = 5`

Multiply both sides by 2.

`9+x_2=10`

Subtract 9 from both sides.

`x_2=1`

Also,

`(1+y_2)/(2) = 5`

Multiply both sides by 2.

`1+y_2=10`

Subtract both sides by 1.

`y_2=9`

So, the point
`(x_2,y_2)`, or point R is (1, 9).