Answer:
The other endpoint is (-33, 17)
Step-by-step explanation:
The rule of the mid-point of a segment whose endpoints are
([tex]x_{1}[/tex], [tex]y_{1}[/tex]) and ([tex]x_{2}[/tex], [tex]y_{2}[/tex]) is
In our question
∵ The coordinates of the endpoints of a segment are (-15, 13) and (x, y)
∴ [tex]x_{1}[/tex] = -15 and [tex]x_{2}[/tex] = x
∴ [tex]y_{1}[/tex] = 13 and [tex]y_{2}[/tex] = y
∵ The coordinates of the mid-point of this segment are (-24, 15)
∴ [tex]x_{M}[/tex] = -24 and [tex]y_{M}[/tex] = 15
→ Use the rule of the mid-point to find x and y
∵ [tex]-24=\frac{-15+x}{2}[/tex]
→ Multiply both sides by 2
∴ -48 = -15 + x
→ Add 15 to both sides
∴ -33 = x
∵ [tex]15=\frac{13+y}{2}[/tex]
→ Multiply both sides by 2
∴ 30 = 13 + y
→ Subtract 13 from both sides
∴ 17 = y
∴ The other endpoint is (-33, 17)
