The co-ordinates of point B is (6, -9)
Solution:
Given that coordinates of endpoint A(2, -3) and the coordinates of midpoint is M(4, -6)
To find: co - ordinates of B
The midpoint m(x, y) is given by formula:
For endpoints [tex]A(x_1, y_1)[/tex] and [tex]B(x_2, y_2)[/tex], midpoint is given by formula:
[tex]m(x, y)=\left(\frac{x_{1}+x_{2}}{2}, \frac{y_{1}+y_{2}}{2}\right)[/tex]
Here in this sum,
[tex](x_1, y_1) = (2, -3)\\\\(x, y) = (4, -6)[/tex]
Substituting the values in above formula,
[tex](4,-6)=\left(\frac{2+x_{2}}{2}, \frac{-3+y_{2}}{2}\right)[/tex]
Comparing the L.H.S and R.H.S, we get
[tex]4=\frac{2+x_{2}}{2} \text { and }-6=\frac{-3+y_{2}}{2}\\\\8 = 2 + x_2 \text{ and } -12 = -3 + y_2\\\\x_2 = 8-2 \text{ and } y_2 = -12+3\\\\x_2 = 6 \text{ and } y_2 = -9[/tex]
Thus co-ordinates of point B is (6, -9)
