Question

M(5, 7) is the midpoint of RS. The coordinates of S are (6, 9). What are the coordinates of R?

Answer 1

Coordinate R is at (4,5)

Answer 2

The coordinates of R are
`(x_1,y_1)=(4,5)`

Explanation:

Given : M(5, 7) is the midpoint of RS. The coordinates of S are (6, 9).

To find : What are the coordinates of R?

Solution :

We have given,

A line RS which has a mid point M.

Let, the coordinates of R be
`(x_1,y_1)`

The coordinates of S are
`(x_2,y_2)=(6, 9)`

The coordinates of M are
`(x_3,y_3)=(5,7)`

Applying mid-point formula,

`(x_3,y_3)=((x_1+x_2)/(2),(y_1+y_2)/(2))`

`(5,7)=((x_1+6)/(2),(y_1+9)/(2))`

Solve separately,

x- coordinate is

`(x_1+6)/(2)=5`

`x_1+6=10`

`x_1=4`

y- coordinate is

`(y_1+9)/(2)=7`

`y_1+9=14`

`y_1=5`

So, The coordinates of R are
`(x_1,y_1)=(4,5)`