Answer:
[tex]B = (8,-6)[/tex]
Step-by-step explanation:
Given
[tex]A = (4,8)[/tex]
[tex]M = (6,1)[/tex] -- Midpoint
Required
Find B
This question will be solved using midpoint formula;
[tex]M(x,y) = (\frac{x_1 + x_2}{2},\frac{y_1 + y_2}{2})[/tex]
Where
[tex]A(x_1,y_1) = (4,8)[/tex]
[tex]M(x,y) = (6,1)[/tex]
Substitute these values in the midpoint formula;
[tex](6,1) = (\frac{4 + x_2}{2},\frac{8+y_2}{2})[/tex]
By comparison; we have:
[tex]\frac{4 + x_2}{2} = 6[/tex] -- (1)
[tex]\frac{8 + y_2}{2} = 1[/tex] -- (2)
Solving (1)
[tex]\frac{4 + x_2}{2} = 6[/tex]
Multiply both sides by 2
[tex]4 + x_2 = 12[/tex]
Subtract 4 from both sides
[tex]x_2 = 8[/tex]
Solving (2)
[tex]\frac{8 + y_2}{2} = 1[/tex]
Multiply both sides by 2
[tex]8 + y_2 = 2[/tex]
Subtract 8 from both sides
[tex]y_2 = -6[/tex]
Hence:
[tex]B = (8,-6)[/tex]
