Question

The coordinates of point S are (8.4). What are the

M 17, 3) is the midpoint of RS
coordinates of R?

Answer 1

Co-ordinates of point R is (26,2)

Step-by-step explanation:

Given point:

Endpoint S(8,4)

Mid-point M of segment RS (17,3)

Let endpoint
`R` have co-ordinates
`(x_2,y_2)`

Using midpoint formula:

`M=((x_1+x_2)/(2),(y_1+y_2)/(2))`

Where
`(x_1,y_1)` and
`(x_2,y_2)` are co-ordinates of the endpoint of the segment.

Plugging in values to find the midpoint of segment KN.

`M=((8+x_2)/(2),(4+y_2)/(2))`

We know
`M(17,3)`

So, we have

`(17,3)=((8+x_2)/(2),(4+y_2)/(2))`

Solving for
`x_2`

`(8+x_2)/(2)=17`

Multiplying both sides by 2.

`(8+x_2)/(2)* 2=17* 2`

`8+x_2=34`

Subtracting both sides by 8.

`8+x_2-8=34-8`

∴
`x_2=26`

Solving for
`y_2`

`(4+y_2)/(2)=3`

Multiplying both sides by 2.

`(4+y_2)/(2)* 2=3* 2`

`4+y_2=6`

Subtracting both sides by 4.

`4+y_2-4=6-4`

∴
`y_2=2`

Thus co-ordinates of point R is (26,2) (Answer)