Question

4. M(7, 3) is the midpoint of RS. The coordinates of point S are (8,4). What are the

coordinates of R?
2Vs
Find SR

Answer 1

The co-ordinates of point R is (6 , 2)

Solution:

Given that M(7, 3) is the midpoint of RS

Also co-ordinates of point S is (8, 4)

To find: co-ordinates of point R

The midpoint of two points
`P(x_1, y_1)` and
`Q(x_2, y_2)` is given as:

`M=\left((x_(1)+x_(2))/(2), (y_(1)+y_(2))/(2)\right)`

Here midpoint M = (7, 3) and point S
`(x_1 , y_1) = (8, 4)`

Point R =
`(x_2, y_2)`

Substituting the values in formula we get,

`(7,3)=\left((8+x_(2))/(2), (4+y_(2))/(2)\right)`

Comparing both the sides we get,

`(8+x_(2))/(2)=7` and
`(4+y_(2))/(2)=3`

On solving,

`\begin{array}{l}{14=8+x_(2)} \\\\ {x_(2)=6}\end{array}`

Also,

`\begin{array}{l}{4+y_(2)=6} \\\\ {y_(2)=2}\end{array}`

Thus the co-ordinates of point R is (6 , 2)