Question

the coordinates of the vertices of the triangle shown are p (2, 13), q (7, 1), and r (2, 1). what is the length of segment pq in units? units

Explanation:

Step1: Recall distance formula

The distance formula between two points $(x_1,y_1)$ and $(x_2,y_2)$ is $d = \sqrt{(x_2 - x_1)^2+(y_2 - y_1)^2}$. For points $P(2,13)$ and $Q(7,1)$, $x_1 = 2,y_1=13,x_2 = 7,y_2 = 1$.

Step2: Calculate differences

First, find $x_2 - x_1$ and $y_2 - y_1$. $x_2 - x_1=7 - 2=5$ and $y_2 - y_1=1 - 13=- 12$.

Step3: Square the differences

Square the results from Step 2. $(x_2 - x_1)^2=5^2 = 25$ and $(y_2 - y_1)^2=(-12)^2=144$.

Step4: Sum the squared differences

Add the squared - differences: $(x_2 - x_1)^2+(y_2 - y_1)^2=25 + 144=169$.

Step5: Take the square - root

$d=\sqrt{169}=13$.

Answer:

13