Question

use the distance formula below to answer the que distance formula ( d = sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2} ) what is the distance between (7, -2) and (3,1)?

Explanation:

Step1: Identify coordinates

Let \((x_1, y_1) = (7, -2)\) and \((x_2, y_2) = (3, 1)\).

Step2: Substitute into distance formula

Substitute into \(d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}\):
\(d = \sqrt{(3 - 7)^2 + (1 - (-2))^2}\)

Step3: Simplify inside the square root

Calculate each term:
\(3 - 7 = -4\), so \((-4)^2 = 16\)
\(1 - (-2) = 3\), so \(3^2 = 9\)
Now, \(d = \sqrt{16 + 9}\)

Step4: Final calculation

\(16 + 9 = 25\), so \(d = \sqrt{25} = 5\)

Answer:

5