Question

Find the coordinates

Answer 1

Given:

The two points are P(14,16) and Q(21,19).

M is the midpoint of the segment PQ.

To find:

The distance between P and Q, and find the coordinates of point M.

Solution:

Distance between P(14,16) and Q(21,19) is

`d=√((x_2-x_1)^2+(y_2-y_1)^2)`

`d(P,Q)=√((21-14)^2+(19-16)^2)`

`d(P,Q)=√((7)^2+(3)^2)`

`d(P,Q)=√(49+9)`

On further simplification, we get

`d(P,Q)=√(58)`

`d(P,Q)=√(58)`

The midpoint of P and Q is M. So, the coordinates of the midpoint are:

`M=\left((x_1+x_2)/(2),(y_1+y_2)/(2)\right)`

`M=\left((14+21)/(2),(16+19)/(2)\right)`

`M=\left((35)/(2),(35)/(2)\right)`

`M=\left(17.5,17.5\right)`

Therefore, the distance between P and Q is
`√(58)` and the midpoint of P and Q is
`M=\left(17.5,17.5\right)`.