Question

given the coordinate of one endpoint of AB and it’s midpoint M, find the coordinates of the other endpoint. A(0,9) M(2,5)

Answer 1

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 $A(x_1, y_1) \text{ and } B(x_2, y_2)$ is given as:

$m(x, y)=\left(\frac{x_{1}+x_{2}}{2}, \frac{y_{1}+y_{2}}{2}\right)$

Here in this sum,

$m(x, y) = (2, 5)\\\\A(x_1, y_1) = (0, 9)\\\\B(x_2, y_2) = ?$

Substituting in above formula, we get

$\begin{aligned}&(2,5)=\left(\frac{0+x_{2}}{2}, \frac{9+y_{2}}{2}\right)\\\\&(2,5)=\left(\frac{x_{2}}{2}, \frac{9+y_{2}}{2}\right)\end{aligned}$

Compare the L.H.S and R.H.S

$2 = \frac{x_2}{2} \text{ and } 5 = \frac{9+y_2}{2}\\\\x_2 = 2 \times 2 \text{ and } 10 = 9 + y_2\\\\x_2 = 4 \text{ and } y_2 = 1$

Thus the co-ordinate of point B is (4, 1)