Question

joanne does a daily walk from building p to building q. given point p(6,9) and point q(5,-4), what is the distance between points p and q on this campus map of the local college?

Explanation:

Step1: Identify 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, $x_1 = 6,y_1 = 9,x_2 = 5,y_2=- 4$.

Step2: Calculate differences

$x_2 - x_1=5 - 6=-1$ and $y_2 - y_1=-4 - 9=-13$.

Step3: Square the differences

$(x_2 - x_1)^2=(-1)^2 = 1$ and $(y_2 - y_1)^2=(-13)^2 = 169$.

Step4: Sum the squared - differences

$(x_2 - x_1)^2+(y_2 - y_1)^2=1 + 169=170$.

Step5: Find the square - root

$d=\sqrt{170}\approx 13.04$.

Answer:

$\sqrt{170}\approx13.04$