If a segment has an endpoint at (-2, -5) and a midpoint at (-5, -1), determine the coordinates of the other endpoint.

Since we know one end point and the midpoint, all we need to do is take the vector from the end point to the midpoint, and add it again to the midpoint to find the other end point:

dx = -5 - (-2) = -3

dy = -1 - (-5) = 4

-5 + dx = -8

-1 + dx = 3

So the other end of the line segment is at (-8, 3)

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Adetunmbiadekunle Adetunmbiadekunle · Answer 2 · 2021-11-26T10:54:49+01:00

If a segment has an endpoint at (-2, -5) and a midpoint at (-5, -1), the coordinates of the other endpoint are (-8, 3)

The midpoint of a line segment is given as:

[tex]a=\frac{x_1+x_2}{2} \\\\b=\frac{y_1+y_2}{2}[/tex]

One of the endpoints of the line segment is (-2, -5)

That is, [tex]x_1=-2, y_1=-5[/tex]

Let the coordinates of the other endpoint be [tex](x_2, y_2)[/tex]

Solving for [tex]x_1[/tex] and [tex]y_1[/tex] in the equation:

[tex]a=\frac{x_1+x_2}{2} \\\\b=\frac{y_1+y_2}{2}[/tex]

[tex]-5=\frac{-2+x_2}{2} \\\\-2+x_2=-5(2)\\\\x_2=-10+2\\\\x_2=-8[/tex]

Solve for [tex]y_2[/tex]

[tex]b=\frac{y_1+y_2}{2} \\\\-1=\frac{-5+y_2}{2} \\\\-2=-5+y_2\\\\y_2=-2+5\\\\y_2=3[/tex]

The coordinates of the other endpoint are (-8, 3)

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