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4. If M is the midpoint of line segment EF. E is located at (10,-8) and M is located at (-6, -2). Find the other
endpoint.

User Bennylope
by
4.2k points

2 Answers

3 votes

Answer:

F = (-22, 4)

Explanation:

Midpoint between two points


\textsf{Midpoint}=\left((x_2+x_1)/(2),(y_2+y_1)/(2)\right)\\\\ \textsf{where $(x_1,y_1)$ and $(x_2,y_2)$ are the endpoints.}

Given information:

  • Midpoint = (-6, -2)
  • E = (10, -8)

Define the endpoints of the line segment EF:

  • Let (x₁, y₁) = endpoint E = (10, -8)
  • Let (x₂, y₂) = endpoint F

Substitute the given information into the formula:


\implies (x_M,y_M)=\left((x_F+x_E)/(2),(y_F+y_E)/(2)\right)


\implies (-6,-2)=\left((x_F+10)/(2),(y_F-8)/(2)\right)

Find the x-coordinate of M:


\implies (x_F+10)/(2)=-6


\implies x_F+10=-12


\implies x_F=-22

Find the y-coordinate of M:


\implies (y_F-8)/(2)=-2


\implies y_F-8=-4


\implies y_F=4

Therefore, the coordinates of endpoint F are (-22, 4).

15 4. If M is the midpoint of line segment EF. E is located at (10,-8) and M is located-example-1
User RobVious
by
4.6k points
0 votes

Answer:

  • The other endpoint is F( - 22, 4)

=============================

Given

Segment EF with:

  • Endpoint E = (10, - 8),
  • Midpoint M = (- 6, - 2),
  • Endpoint F = (x, y).

Solution

Use midpoint equation:

  • x = (x₁ + x₂)/2, y = (y₁ + y₂)/2

Find unknown coordinates of the point F:

  • - 6 = (10 + x)/2 ⇒ -12 = 10 + x ⇒ x = - 12 - 10 = - 22,
  • - 2 = (- 8 + y)/2 ⇒ - 4 = - 8 + y ⇒ y = - 4 + 8 = 4.

So the point is F = ( - 22, 4)

User BlackMagic
by
3.4k points