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

$d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}$

$d(P,Q)=\sqrt{(21-14)^2+(19-16)^2}$

$d(P,Q)=\sqrt{(7)^2+(3)^2}$

$d(P,Q)=\sqrt{49+9}$

On further simplification, we get

$d(P,Q)=\sqrt{58}$

$d(P,Q)=\sqrt{58}$

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

$M=\left(\dfrac{x_1+x_2}{2},\dfrac{y_1+y_2}{2}\right)$

$M=\left(\dfrac{14+21}{2},\dfrac{16+19}{2}\right)$

$M=\left(\dfrac{35}{2},\dfrac{35}{2}\right)$

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

Therefore, the distance between P and Q is $\sqrt{58}$ and the midpoint of P and Q is $M=\left(17.5,17.5\right)$.