Question

M is the midpoint of RS. R has coordinates (-2,-3) and M has coordinates (1,0). Find the coordinates of S.

Answer 1

`(4,3)`

Explanation:

Given

`R = (-2,-3)`

`M = (1,0)`

Required

Determine the coordinates of S

Midpoint is calculated as:

`M(x,y) = (1)/(2)(x_1 +x_2,y_1+y_2)`

Where:

`(x,y) = (1,0)`

`(x_1,y_1) = (-2,-3)`

Substitute these values in the above formula:

`(1,0) = (1)/(2)(-2 + x_2,-3+y_2)`

Multiply through by 2

`2 * (1,0) = 2 * (1)/(2)(-2 + x_2,-3+y_2)`

`(2,0) = (-2 + x_2,-3+y_2)`

By direct comparison:

`2 = -2 + x_2` and
`0 = -3 + y_2`

Solving for x2

`2 = -2 + x_2`

`x_2 = 2 + 2`

`x_2 = 4`

Solving for y2

`0 = -3 + y_2`

`y_2 = 0 + 3`

`y_2 = 3`

Hence, the coordinates of S is:
`(4,3)`