Question

for the pair of points find the distance between them and the midpoint of the line segment joining them. (18, - 2) and (3,18)
the distance is
(simplify your answer.)
the midpoint is
(type an ordered pair. simplify your answer.)

Explanation:

Step1: Recall distance formula

The distance $d$ between two points $(x_1,y_1)$ and $(x_2,y_2)$ is $d = \sqrt{(x_2 - x_1)^2+(y_2 - y_1)^2}$. Here, $x_1 = 18,y_1=-2,x_2 = 3,y_2 = 18$.
$d=\sqrt{(3 - 18)^2+(18-(-2))^2}$

Step2: Calculate the values inside the square - root

$(3 - 18)^2=(-15)^2 = 225$ and $(18-(-2))^2=(18 + 2)^2=20^2 = 400$. Then $d=\sqrt{225 + 400}=\sqrt{625}=25$.

Step3: Recall mid - point formula

The mid - point $M$ of the line segment joining two points $(x_1,y_1)$ and $(x_2,y_2)$ is $M=(\frac{x_1 + x_2}{2},\frac{y_1 + y_2}{2})$.
$M=(\frac{18 + 3}{2},\frac{-2+18}{2})$

Step4: Calculate the mid - point coordinates

$\frac{18 + 3}{2}=\frac{21}{2}=10.5$ and $\frac{-2 + 18}{2}=\frac{16}{2}=8$. So the mid - point is $(10.5,8)$.

Answer:

The distance is $25$.
The midpoint is $(10.5,8)$