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Liula [17]
3 years ago
14

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.)​
Mathematics
1 answer:
kiruha [24]3 years ago
5 0

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)

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