Question

Find the coordinates of endpoint B, given the coordinates of endpoint A(2, -3) and the coordinates of midpoint is M(4, -6).

Answer 1

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
`A(x_1, y_1)` and
`B(x_2, y_2)`, midpoint is given by formula:

`m(x, y)=\left((x_(1)+x_(2))/(2), (y_(1)+y_(2))/(2)\right)`

Here in this sum,

`(x_1, y_1) = (2, -3)\\\\(x, y) = (4, -6)`

Substituting the values in above formula,

`(4,-6)=\left((2+x_(2))/(2), (-3+y_(2))/(2)\right)`

Comparing the L.H.S and R.H.S, we get

`4=(2+x_(2))/(2) \text { and }-6=(-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`

Thus co-ordinates of point B is (6, -9)