Question

Find the other endpoint of a line segment which one endpoint at (-3, 5) and whose midpoint is (5, 2)

Answer 1

Let the unknown endpoint be (x₂ , y₂) and the known (x₁ , y₁)

mid-point =
`( (x_(1) + x_(2) )/(2) , (y_(1) + y_(2) )/(2) )` = (A , B)
plug in the known values

=>
`( (-3 + x_(2) )/(2) , (5 + y_(2) )/(2) )`

separate the two parts of the equation for the formula and solve
for the value of the unknown y and x

=> A :
`(-3 + x_(2) )/(2) = 5`
-3 + x₂ = (5)(2)
x₂ = 10 + 3
= 13

B:
`(5 + y_(2) )/(2) = 2`
5 + y₂ = (2)(2)
5 + y₂ = 4
y₂ = 4 - 5
= - 1

∴ if midpoint is (A,B) then midpoint is (13 , -1)

Answer 2

so to find the other endpoint you need to see how far the first endpoint is to the midpoint. In X's place we have a total distance of
5- (-3)= 8 place away from one another so
5+8= 13

while in the y's case
5-2=3 place away from one another so
2-3= -1

so your order pair is
(13,-1)