Answer:
[tex](8,-4)[/tex]
Step-by-step explanation:
Given
[tex]A = (3,4)[/tex]
[tex]M = (5.5,0)[/tex]---- Midpoint
Required
[tex]Find\ B[/tex]
This will be solved using Midpoint formula:
[tex](x,y) = (\frac{x_1 + x_2}{2},\frac{y_1 + y_2}{2})[/tex]
Where
[tex](x,y) = M(5.5,0)[/tex]
[tex](x_1, y_1) = A(3,4)[/tex]
Substitute these values, then we have:
[tex](5.5,0) = (\frac{3 + x_2}{2},\frac{4 + y_2}{2})[/tex]
Compare the right hand side with the left, we have
[tex]5.5 = \frac{3 + x_2}{2}[/tex] --- (1)
[tex]0 = \frac{4 + y_2}{2}[/tex] --- (2)
Solving (1)
[tex]5.5 = \frac{3 + x_2}{2}[/tex]
Multiply both sides by 2
[tex]11 = 3+x_2[/tex]
Subtract 3 from both sides
[tex]x_2 = 11 - 3[/tex]
[tex]x_2 = 8[/tex]
Solving (2)
[tex]0 = \frac{4 + y_2}{2}[/tex]
Multiply both sides by 2
[tex]0 = 4 + y_2[/tex]
Subtract 4 from both sides
[tex]y_2 = 0 - 4[/tex]
[tex]y_2 = - 4[/tex]
Hence:
[tex]B(x_2,y_2) = (8,-4)[/tex]
