Coordinate of the endpoint B is equals to (1,-3) as per given midpoint and one endpoint.
What is midpoint?
" Midpoint is defined as the point which divides the line segment into two equal parts."
Formula used
Endpoints with coordinates are
[tex]A(x_{1}, y_{1})[/tex] and [tex]B(x_{2}, y_{2})[/tex]
Midpoints coordinates are
[tex]M(x,y) = (\frac{x_{1}+x_{2}}{2} , \frac{y_{1}+y_{2}}{2})[/tex]
According to the question,
Given coordinates of line segment AB,
Coordinates of endpoints [tex]A (-5,7)[/tex]
Coordinates of midpoints [tex]M (-2,2)[/tex]
Substitute the value in the formula of midpoint we get,
[tex]M(-2,2) = (\frac{-5+x_{2}}{2} , \frac{7+y_{2}}{2})[/tex]
For [tex]x_{2}[/tex] coordinate
[tex]-2 = \frac{-5+x_{2} }{2}[/tex]
⇒ [tex]x_{2} = -4+5[/tex]
⇒ [tex]x_{2} =1[/tex]
For [tex]y_{2}[/tex] coordinate
[tex]2 = \frac{7+x_{2} }{2}[/tex]
⇒ [tex]y_{2} =4-7[/tex]
⇒ [tex]x_{2} =-3[/tex]
Hence, coordinate of the endpoint B is equals to (1,-3) as per given midpoint and one endpoint.
Learn more about midpoint here
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