Question

(a) find the distance between p and q. (b) find the coordinates of the mid - point of the segment joining p and q. p(-8,2) q(4,6) the distance between p and q is . (simplify your answer. type an exact answer, using radicals as needed.) the mid - point of the segment joining p and q is . (type an ordered pair.)

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, $P(- 8,2)$ so $x_1=-8,y_1 = 2$ and $Q(4,6)$ so $x_2 = 4,y_2=6$.

Step2: Substitute values into formula

$d=\sqrt{(4-(-8))^2+(6 - 2)^2}=\sqrt{(4 + 8)^2+4^2}=\sqrt{12^2+4^2}=\sqrt{144 + 16}=\sqrt{160}=4\sqrt{10}$.

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 $M=(\frac{x_1+x_2}{2},\frac{y_1+y_2}{2})$.

Step4: Substitute values into mid - point formula

$M=(\frac{-8 + 4}{2},\frac{2+6}{2})=(\frac{-4}{2},\frac{8}{2})=(-2,4)$.

Answer:

The distance between $P$ and $Q$ is $4\sqrt{10}$.
The midpoint of the segment joining $P$ and $Q$ is $(-2,4)$.