Question

What is the midpoint and distance between points P(3,5) and Q(7,5)

Answer 1

The formula of a midpoint:

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

The formula of a distance between two points:

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

We have the points P(3, 5) and Q(7, 5). Substitute:

$x=\dfrac{3+7}{2}=\dfrac{10}{2}=5\\\\y=\dfrac{5+5}{2}=\dfrac{10}{2}=5$

M(5, 5)

$d=\sqrt{(5-5)^2+(7-3)^2}=\sqrt{0^2+4^2}=\sqrt{4^2}=4$

Answer:

Midpoint = (5, 5)

Distance = 4