The coordinates of endpoint V is (7, -27) if one endpoint is U(3,5) and the midpoint of UV is (5, -11)
Midpoint of a line is a point that divides any line into two equal parts.
The midpoint of two coordinates (x1, y1) and (x2, y2) is expressed as:
[tex]M(X, Y)= (\frac{x_1+x_2}{2}, \frac{y_1+y_2}{2} )[/tex]
Given the following
midpoint of UV = (5, -11)
U = (3, 5)
Get the other coordinate x2 and y2
Based on the formula above:
[tex]X = \frac{x_1+x_2}{2}\\5=\frac{3+x_2}{2}\\10 = 3 + x_2\\x_2 = 10-3\\x_2 = 7[/tex]
Get the other coordinate x2
[tex]Y = \frac{y_1+y_2}{2}\\-11=\frac{5+y_2}{2}\\-22 = 5 + y_2\\y_2 = -22-5\\y_2 = -27[/tex]
This shows that the coordinates of endpoint V is (7, -27)
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