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

Answer:

The other endpoint is (-33, 17)

Step-by-step explanation:

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

($x_{1}$, $y_{1}$) and ($x_{2}$, $y_{2}$) is

• $(x_{M},y_{M}) = (\frac{x_{1}+x_{2}}{2},\frac{y_{1}+y_{2}}{2})$

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

∵ $-24=\frac{-15+x}{2}$

→ Multiply both sides by 2

∴ -48 = -15 + x

→ Add 15 to both sides

∴ -33 = x

∵ $15=\frac{13+y}{2}$

→ Multiply both sides by 2

∴ 30 = 13 + y

→ Subtract 13 from both sides

∴ 17 = y

∴ The other endpoint is (-33, 17)