Question

observe the figure shown to the right. (a) find the distance between p and q. (b) find the the coordinates of the midpoint of the segment joining p and q. (a) the distance between p and q is . (simplify your answer. type an exact answer, using radicals as needed.)

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, $x_1=-3,y_1 = 2,x_2=3,y_2 = 4$.

Step2: Substitute values

$d=\sqrt{(3-(-3))^2+(4 - 2)^2}=\sqrt{(3 + 3)^2+2^2}=\sqrt{6^2+2^2}=\sqrt{36 + 4}=\sqrt{40}=2\sqrt{10}$.

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

$M=(\frac{-3+3}{2},\frac{2 + 4}{2})=(0,3)$.

Answer:

(a) $2\sqrt{10}$
(b) $(0,3)$