For the point P(-24,-24) and Q(-19,-19), find the distance d(P,Q) and theof the midpoint M of the segment PQ,coordinates

Answer :

Solution:

Given;

[tex]P(-24,-24),Q(-19,-19)[/tex]

The distance d(P,Q) is;

[tex]\begin{gathered} d=\sqrt{(y_2-y_1)^2+(x_2-x_1)^2} \\ \\ x_1=-24,y_1=-24,x_2=-19,y_2=-19 \\ \\ d=\sqrt{(-19-(-24))^2+(-19-(-24))^2} \\ \\ d=\sqrt{50} \\ \\ d=5\sqrt{2} \end{gathered}[/tex]

Also, the midpoint, M, is;

[tex]\begin{gathered} M=(\frac{x_1+x_2}{2},\frac{y_1+y_2}{2}) \\ \\ M=(\frac{-24+(-19)}{2},\frac{-24+(-19)}{2}) \\ \\ M=(-\frac{43}{2},-\frac{43}{2}) \end{gathered}[/tex]