maddie0331838 maddie0331838
  • 23-06-2020
  • Mathematics
contestada


IF (-6, 4) is the endpoint of a line segment, and (-2, -1) is its midpoint, find the other endpoint.
A) (2,-6)
B) (-14, 14)
9 (-16, 12)
D) (2,9)

Respuesta :

r3t40
r3t40 r3t40
  • 23-06-2020

A midpoint has coordinates of [tex](-2, -1)[/tex] we will call them [tex](x_m, y_m)[/tex].

The coordinates of a midpoint are constructed from coordinates of enpoints [tex](x_1,y_1),(x_2,y_2)[/tex], namely as a divided sum.

[tex]

x_m=\frac{x_1+x_2}{2}\implies x_1=2x_m-x_2 \\

y_m=\frac{y_1+y_2}{2}\implies y_1=2y_m-y_2

[/tex]

Now insert the numbers.

[tex]

x_1=2(-2)-(-6)=2 \\

y_1=2(-1)-4=-6

[/tex]

The result is an endpoint at [tex](2,-6)[/tex].

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