Question

find the distance between p and q. the distance between p and q is □. (simplify your answer. type an exact answer, using radicals as needed.) p(-6,7) q(4,9)

Explanation:

Step1: Identify the distance - formula

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

Step2: Determine the coordinates of points P and Q

For point $P(-6,7)$, $x_1=-6$ and $y_1 = 7$. For point $Q(4,9)$, $x_2 = 4$ and $y_2=9$.

Step3: Substitute the values into the formula

$d=\sqrt{(4-(-6))^2+(9 - 7)^2}=\sqrt{(4 + 6)^2+(9 - 7)^2}=\sqrt{10^2+2^2}$.

Step4: Simplify the expression

$d=\sqrt{100 + 4}=\sqrt{104}=\sqrt{4\times26}=2\sqrt{26}$.

Answer:

$2\sqrt{26}$