Question

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

Explanation:

Step1: Identify coordinates of P and Q

Point \( P \) has coordinates \( (2, 13) \) and point \( Q \) has coordinates \( (7, 1) \).

Step2: Apply distance formula

The distance formula between two points \( (x_1, y_1) \) and \( (x_2, y_2) \) is \( d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2} \).
Substitute \( x_1 = 2 \), \( y_1 = 13 \), \( x_2 = 7 \), \( y_2 = 1 \) into the formula:
\[

$$\begin{align*} d &= \sqrt{(7 - 2)^2 + (1 - 13)^2}\\ &= \sqrt{(5)^2 + (-12)^2}\\ &= \sqrt{25 + 144}\\ &= \sqrt{169}\\ &= 13 \end{align*}$$

\]

Answer:

13