Answer:
[tex]B = (0,3)[/tex]
Explanation:
Given
[tex]A=(4,0)[/tex]
[tex]M = (2,1.5)[/tex]
Required
Find B
Since M is the midpoint of AB, we make use of midpoint formula to solve this question
[tex]M(x,y) = (\frac{x_1+x_2}{2}.\frac{y_1+y_2}{2})[/tex]
Where
[tex]A(x_1,y_1) = (4,0)[/tex]
[tex]M(x,y) = (2,1.5)[/tex]
So, we have:
[tex](2,1.5) = (\frac{4+x_2}{2},\frac{0+y_2}{2})[/tex]
Multiply through by 2
[tex](4,3) = (4+x_2,0+y_2)[/tex]
[tex](4,3) = (4+x_2,y_2)[/tex]
By comparison:
[tex]4 = 4 + x_2[/tex] and [tex]3 = y_2[/tex]
Solve for x2
[tex]4 = 4 + x_2[/tex]
[tex]x_2=4-4[/tex]
[tex]x_2=0[/tex]
[tex]y_2 = 3[/tex]
Hence, the coordinates of B is: [tex](0,3)[/tex]
