Respuesta :

mhanifa

Answer:

  • The other endpoint is  F( - 22, 4)

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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)

semsee45

Answer:

F = (-22, 4)

Step-by-step explanation:

Midpoint between two points

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

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:

[tex]\implies (x_M,y_M)=\left(\dfrac{x_F+x_E}{2},\dfrac{y_F+y_E}{2}\right)[/tex]

[tex]\implies (-6,-2)=\left(\dfrac{x_F+10}{2},\dfrac{y_F-8}{2}\right)[/tex]

Find the x-coordinate of M:

[tex]\implies \dfrac{x_F+10}{2}=-6[/tex]

[tex]\implies x_F+10=-12[/tex]

[tex]\implies x_F=-22[/tex]

Find the y-coordinate of M:

[tex]\implies \dfrac{y_F-8}{2}=-2[/tex]

[tex]\implies y_F-8=-4[/tex]

[tex]\implies y_F=4[/tex]

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

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