Question

use the triangle shown to answer the question. what is the length of $overline{pq}$? a. 8 b. 9 c. 10 d. 11

Explanation:

Step1: Identify coordinates

Let \(P=(2,1)\) and \(Q=(10,7)\).

Step2: Apply distance formula

The distance formula between two points \((x_1,y_1)\) and \((x_2,y_2)\) is \(d = \sqrt{(x_2 - x_1)^2+(y_2 - y_1)^2}\). Here \(x_1 = 2,y_1=1,x_2 = 10,y_2 = 7\). So \(d=\sqrt{(10 - 2)^2+(7 - 1)^2}=\sqrt{8^2+6^2}\).

Step3: Calculate values

\(\sqrt{8^2+6^2}=\sqrt{64 + 36}=\sqrt{100}=10\).

Answer:

C. 10