Question

Midpoint (-19,-18) endpoint (-14,-19)

Answer 1

Co-ordinates of endpoint is (-24,-17)

Explanation:

The question should be given as :

Find the coordinates of the other endpoint of the segment, given its midpoint (-19,-18) and one endpoint (-14,-19).

Step-by-step explanation:

Given point:

Endpoint (-14,-19)

Mid-point of segment (-19,-18)

Let endpoint 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.

`M=((-14+x_2)/(2),(-19+y_2)/(2))`

We know
`M(-19,-18)`

So, we have

`(-19,-18)=((-14+x_2)/(2),(-19+y_2)/(2))`

Solving for
`x_2`

`(-14+x_2)/(2)=-19`

Multiplying both sides by 2.

`(-14+x_2)/(2)* 2=-19* 2`

`-14+x_2=-38`

Adding both sides by 14.

`-14+x_2+14=-38+14`

∴
`x_2=-24`

Solving for
`y_2`

`(-19+y_2)/(2)=-18`

Multiplying both sides by 2.

`(-19+y_2)/(2)* 2=-18* 2`

`-19+y_2=-36`

Adding both sides by 19.

`-19+y_2+19=-36+19`

∴
`y_2=-17`

Thus co-ordinates of point N is (-24,-17)