Question

One end of a line segment has the coordinates (-6,2). If

the midpoint is (5,2), then what are the coordinates of the
other endpoint?

Answer 1

The coordinates of the other end is
`(16,2)`

Explanation:

Given

`End 1: (-6,2)`

`Midpoint: (5,2)`

Required

Find the coordinates of the other end

Let Midpoint be represented by (x,y);

(x,y) = (5,2) is calculated as thus

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

So

`x = (x_1 + x_2)/(2)` and
`y = (y_1 + y_2)/(2)`

Where
`(x_1,y_1) = (-6,2)` and
`(x,y) = (5,2)`

So, we're solving for
`(x_2,y_2)`

Solving for
`x_2`

`x = (x_1 + x_2)/(2)`

Substitute 5 for x and -6 for x₁

`5 = (-6 + x_2)/(2)`

Multiply both sides by 2

`2 * 5 = (-6 + x_2)/(2) * 2`

`10 = -6 + x_2`

Add 6 to both sides

`6 + 10 = -6 +6 + x_2`

`x_2 = 16`

Solving for
`y_2`

`y = (y_1 + y_2)/(2)`

Substitute 2 for y and 2 for y₁

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

Multiply both sides by 2

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

`4 = 2 + y_2`

Subtract 2 from both sides

`4 - 2 = 2 - 2 + y_2`

`y_2 = 2`

`(x_2,y_2) = (16,2)`

Hence, the coordinates of the other end is
`(16,2)`