Question

(a) find the distance between p and q. (b) find the coordinates of the mid - point of the segment joining p and q. 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.) p(-10,2) q(6,6)

Explanation:

Step1: Recall distance formula

The distance formula 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, $P(-10,2)$ so $x_1=-10,y_1 = 2$ and $Q(6,6)$ so $x_2 = 6,y_2=6$.

Step2: Substitute values into distance formula

$d=\sqrt{(6-(-10))^2+(6 - 2)^2}=\sqrt{(6 + 10)^2+(4)^2}=\sqrt{(16)^2+16}=\sqrt{256+16}=\sqrt{272}=\sqrt{16\times17}=4\sqrt{17}$.

Step3: Recall mid - point formula

The mid - point formula between 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

$M=(\frac{-10 + 6}{2},\frac{2+6}{2})=(\frac{-4}{2},\frac{8}{2})=(-2,4)$.

Answer:

The distance between $P$ and $Q$ is $4\sqrt{17}$.
The midpoint of the segment joining $P$ and $Q$ is $(-2,4)$.