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