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The midpoint of the line segment from P₁ to P₂ is (-4,1), If P₁ =(-1,4), what is P₂?

User Yujuezhao
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1 Answer

1 vote

Answer:

P2 = (-7, -2)

Explanation:

The midpoint formula is given by:

M = (x1 + x2) / 2, (y1 + y2) / 2, where

  • M are the coordinates of the midpoint,
  • (x1, y1) is one endpoint of the line segment,
  • and (x2, y2) is another endpoint.

Since we're already given the midpoint and one of the endpoints, we can find the coordinates of the other endpoint by using (-4, 1) for M and (-1, 4) for (x1, y1):

x-coordinate of P2:

To find the x-coordinate of P2 (aka x2 in the midpoint formula), we plug in -4 for M and -1 for x1:

(-4 = (-1 + x2) / 2) * 2

(-8 = -1 + x2) + 1

-7 = x2

Thus, the x-coordinate of P2 is -7.

y-coordinate of P2:

To find the y-coordinate of P2 (aka y2 in the midpoint formula), we plug in 1 for M and 4 for x1:

(1 = (4 + y2) / 2) * 2

(2 = 4 + y2) - 4

-2 = y2

Thus, the y-coordinate of P2 is -2.

Therefore, the coordinates of P2 are (-7, -2)

User Krunal Vaghela
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