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
[tex]d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]
[tex]d(P,Q)=\sqrt{(21-14)^2+(19-16)^2}[/tex]
[tex]d(P,Q)=\sqrt{(7)^2+(3)^2}[/tex]
[tex]d(P,Q)=\sqrt{49+9}[/tex]
On further simplification, we get
[tex]d(P,Q)=\sqrt{58}[/tex]
[tex]d(P,Q)=\sqrt{58}[/tex]
The midpoint of P and Q is M. So, the coordinates of the midpoint are:
[tex]M=\left(\dfrac{x_1+x_2}{2},\dfrac{y_1+y_2}{2}\right)[/tex]
[tex]M=\left(\dfrac{14+21}{2},\dfrac{16+19}{2}\right)[/tex]
[tex]M=\left(\dfrac{35}{2},\dfrac{35}{2}\right)[/tex]
[tex]M=\left(17.5,17.5\right)[/tex]
Therefore, the distance between P and Q is [tex]\sqrt{58}[/tex] and the midpoint of P and Q is [tex]M=\left(17.5,17.5\right)[/tex].
