Question

The length of a line segment is 13 units. One end point of the line segment is -3,7. Find four points that could be the other end points of the line segment

Answer 1

The points are (-16,7),(10,7),(-3,-6) and (-3,20)

Explanation:

We have that one endpoint is at (-3,7) and the length is 13 units.

A point that is 13 units horizontally to the left and right will have the same y-coordinate but with x-coordinates that are 13 units from -3.

`| - 3 - x| = 13`

`( - 3 - x) = 13 \: or \: - ( - 3 - x) = 13`

`x = - 16 \: or \: x = 10`

Hence we have (-16,7) and (10,7)

Also a point that is 13 units vertically up and down will have the same x-coordinate but with y-coordinates that are 13 units from 7.

`|y - 7| = 13`

`(y - 7) = 13 \: or \: - (y - 7) = 13`

`y= - 6 \: or \: y = 20`

Hence we again have (-3,-6) and (-3,20)