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The midpoint of a line segment is (−3,2). One endpoint of the line segment is (4,−7).

What are the coordinates of the other endpoint of the line segment?

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Answer:

The other endpoint is  (9, −6)

Step-by-step explanation:

(x1,y1)=(3,2) and M=(6,−2)

x1+x22=x     and     y1+y22=y

3+x22=6     and     2+y22=−2     ←×2

3+x2=12     and     2+y2=−4

x2=9              and     y2=−6

xero099

The coordinates of the other endpoint of the line segment are [tex]Y(x,y) = (-10, 11)[/tex].

Vectorially speaking, the midpoint of a line segment is determined by the following expression:

[tex]M(x,y) = \frac{1}{2}\cdot X(x,y) + \frac{1}{2}\cdot Y(x,y)[/tex] (1)

Where:

  • [tex]M(x,y)[/tex] - Midpoint.
  • [tex]X(x,y)[/tex], [tex]Y(x,y)[/tex] - Endpoints of the line segment.

If we know that [tex]M(x,y) = (-3, 2)[/tex] and [tex]X(x,y) = (4, -7)[/tex], then the coordinates of the other endpoint is:

[tex]\frac{1}{2}\cdot Y(x,y) = M(x,y) -\frac{1}{2}\cdot X(x,y)[/tex]

[tex]Y(x,y) = 2\cdot M(x,y) -X(x,y)[/tex]

[tex]Y(x,y) = 2\cdot (-3,2)-(4,-7)[/tex]

[tex]Y(x,y) = (-6, 4) - (4, -7)[/tex]

[tex]Y(x,y) = (-10, 11)[/tex]

The coordinates of the other endpoint of the line segment are [tex]Y(x,y) = (-10, 11)[/tex].

We kindly invite to check this question on midpoints: https://brainly.com/question/17506315

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