The midpoint of a line segment divides the line segment into equal halves. The point of B is (7,2)
Given that:
[tex]A = (-1,6)[/tex]
[tex]M = (3,4)[/tex]
Point B is represented as:
[tex]B = (x_2,y_2)[/tex]
To calculate the coordinate of B, we use the following midpoint formula:
[tex]M = (\frac{x_1 + x_2}{2},\frac{y_1 + y_2}{2})[/tex]
So, we have:
[tex](3,4) = (\frac{-1 + x_2}{2},\frac{6 + y_2}{2})[/tex]
Multiply through by 2
[tex]2 \times (3,4) = (-1 + x_2,6 + y_2)[/tex]
[tex](6,8) = (-1 + x_2,6 + y_2)[/tex]
By comparison:
[tex]6 = -1 +x_2[/tex] and
[tex]8 = 6 + y_2[/tex]
So, we have:
[tex]6 = -1 +x_2[/tex]
[tex]x_2 =6 + 1[/tex]
[tex]x_2 =7[/tex]
[tex]8 = 6 + y_2[/tex]
[tex]y_2 = 8 - 6[/tex]
[tex]y_2 = 2[/tex]
Hence, the coordinate of B is (7,2)
Read more about midpoints at:
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