Question

Find the coordinates of the other endpoint of the segment, given its midpoint and one endpoint. (Hint: Let (x,y) be the unknown endpoint. Apply the midpoint formula, and solve the two equations for x and y.) midpoint (-24,15), endpoint (- 15,13) The other endpoint is (Type an ordered pair.)​

Answer 1

The other endpoint is (-33, 17)

Explanation:

The rule of the mid-point of a segment whose endpoints are

(
`x_(1)`,
`y_(1)`) and (
`x_(2)`,
`y_(2)`) is

• 
  `(x_(M),y_(M)) = ((x_(1)+x_(2))/(2),(y_(1)+y_(2))/(2))`

In our question

∵ The coordinates of the endpoints of a segment are (-15, 13) and (x, y)

∴
`x_(1)` = -15 and
`x_(2)` = x

∴
`y_(1)` = 13 and
`y_(2)` = y

∵ The coordinates of the mid-point of this segment are (-24, 15)

∴
`x_(M)` = -24 and
`y_(M)` = 15

→ Use the rule of the mid-point to find x and y

∵
`-24=(-15+x)/(2)`

→ Multiply both sides by 2

∴ -48 = -15 + x

→ Add 15 to both sides

∴ -33 = x

∵
`15=(13+y)/(2)`

→ Multiply both sides by 2

∴ 30 = 13 + y

→ Subtract 13 from both sides

∴ 17 = y

∴ The other endpoint is (-33, 17)