The midpoint of line segment mn is located at (-5,-8). the endpoint m is located at (3,4). what are the coordinates of endpoint n?

The coordinates of point N are (-13 , -20)

Step-by-step explanation:

* Lets revise how to find the mid-point of a segment

- If a line has two endpoints(x1 , y1) and (x2 , y2), then we can find

 the mid-point (x , y) of it by using this rule

 x = (x1 + x2)/2  and y = (y1 + y2)/2

* Now lets solve the problem

∵ The line segment is MN

∵ M is (3 , 4)

∵ The mid-point is (-5 , -8)

- Let M is (x1 , y1) and N is (x2 , y2)

- Let the mid-point is (x , y)

∴ x1 = 3 , y1 = 4

∴ x = -5 , y = -8

∵ x = (x1 + x2)/2

∴ -5 = (3 + x2)/2 ⇒ multiply both sides by 2

∴ -10 = 3 + x2 ⇒ subtract 3 from both sides

∴ x2 = -13

∵ y = (y1 + y2)/2

∴ -8 = (4 + y2)/2 ⇒ multiply both sides by 2

∴ -16 = 4 + y2 ⇒ subtract 4 from both sides

∴ y2 = -20

∴ The coordinates of point N are (-13 , -20)

the answer is a

step-by-step explanation: