Question

calculating triangle side lengths in the coordinate plane

1. use the distance formula to find the lengths of the sides of the second triangle, triangle pqr.

\\(3, 4, 5\\)
\\(\sqrt{13}, \sqrt{10}, 3\\)
\\(9, 16, 25\\)
\\(3\sqrt{13}, 3\sqrt{10}, 9\\)

Explanation:

Identify the coordinates of triangle PQR

$$ P(2, 2), \quad Q(0, -1), \quad R(-1, 2) $$

Calculate the side lengths using the distance formula

$$
LATEXBLOCK0
$$

Match with the given options

$$ \text{Side lengths: } \sqrt{13}, \sqrt{10}, 3 $$

Answer:

• (A) \(3, 4, 5\)
• (B) \(\sqrt{13}, \sqrt{10}, 3\) (Correct answer)
• (C) \(9, 16, 25\)
• (D) \(3\sqrt{13}, 3\sqrt{10}, 9\)