The co-ordinate of point B is (4, 1)
Solution:
Given the coordinate of one endpoint of AB and it’s midpoint M , A(0, 9) M(2, 5)
To find: co-ordinate of endpoint B
The midpoint m(x, y) of points [tex]A(x_1, y_1) \text{ and } B(x_2, y_2)[/tex] is given as:
[tex]m(x, y)=\left(\frac{x_{1}+x_{2}}{2}, \frac{y_{1}+y_{2}}{2}\right)[/tex]
Here in this sum,
[tex]m(x, y) = (2, 5)\\\\A(x_1, y_1) = (0, 9)\\\\B(x_2, y_2) = ?[/tex]
Substituting in above formula, we get
[tex]\begin{aligned}&(2,5)=\left(\frac{0+x_{2}}{2}, \frac{9+y_{2}}{2}\right)\\\\&(2,5)=\left(\frac{x_{2}}{2}, \frac{9+y_{2}}{2}\right)\end{aligned}[/tex]
Compare the L.H.S and R.H.S
[tex]2 = \frac{x_2}{2} \text{ and } 5 = \frac{9+y_2}{2}\\\\x_2 = 2 \times 2 \text{ and } 10 = 9 + y_2\\\\x_2 = 4 \text{ and } y_2 = 1[/tex]
Thus the co-ordinate of point B is (4, 1)
