Question

The midpoint of the segment connecting the points labeled K and N has coordinates (5, -4). If the coordinates of point K are (7, -2) then what are the coordinates of point N?​

Answer 1

Co-ordinates of point N is (3,-6)

Explanation:

Given point:

Endpoint K(7,-2)

Mid-point of segment KN (5,-4)

Let endpoint
`N` 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=((7+x_2)/(2),(-2+y_2)/(2))`

We know
`M(5,-4)`

So, we have

`(5,-4)=((7+x_2)/(2),(-2+y_2)/(2))`

Solving for
`x_2`

`(7+x_2)/(2)=5`

Multiplying both sides by 2.

`(7+x_2)/(2)* 2=5* 2`

`7+x_2=10`

Subtracting both sides by 7.

`7+x_2-7=10-7`

∴
`x_2=3`

Solving for
`y_2`

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

Multiplying both sides by 2.

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

`-2+y_2=-8`

Adding both sides by 2.

`-2+y_2+2=-8+2`

∴
`y_2=-6`

Thus co-ordinates of point N is (3,-6)