GabbiL
contestada

which is the other endpoint of a line segment with one endpoint at (-2,-5) and midpoint at (3,2)

(A). (1,-3)
(B). (2,-6)
(C). (5,7)
(D). (8,9)
(E). (10,14)

Respuesta :

[tex]\bf ~~~~~~~~~~~~\textit{middle point of 2 points } \\\\ (\stackrel{x_1}{-2}~,~\stackrel{y_1}{-5})\qquad (\stackrel{x_2}{x}~,~\stackrel{y_2}{y}) \qquad \left(\cfrac{ x_2 + x_1}{2}~~~ ,~~~ \cfrac{ y_2 + y_1}{2} \right) \\\\\\ \left( \cfrac{x-2}{2}~~,~~\cfrac{y-5}{2} \right)~=~\stackrel{midpoint}{(3,2)}\implies \begin{cases} \cfrac{x-2}{2}=3\\[1em] x-2=6\\ \boxed{x=8}\\[-0.5em] \hrulefill\\ \cfrac{y-5}{2}=2\\[1em] y-5=4\\ \boxed{y=9} \end{cases}[/tex]

akposevictor

Using the midpoint formula, the coordinates of the other endpoint is: D. (8, 9).

What is the Midpoint Formula?

Midpoint formula is given as, M(x, y) = [tex](\frac{x_2 + x_1}{2}, \frac{y_2 + y_1}{2} )[/tex]

Given:

  • M(3, 2)
  • (-2, -5) = (x1, y1)
  • (?, ?) = (x2, y2)

Plug in the values into the midpoint formula:

M(3, 2) = [tex](\frac{x_2 -2}{2}, \frac{y_2 - 5}{2} )[/tex]

3 = (x2 - 2)/2

2(3) = x2 - 2

6 = x2 - 2

6 + 2 = x2

x2 = 8

2 = (y2 - 5)/2

2(2) = y2 - 5

4 = y2 - 5

4 + 5 = y2

y2 = 9

The other endpoint is: D. (8, 9)

Learn more about the midpoint formula on:

https://brainly.com/question/13115533

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