Question

graph a right triangle with the two points forming the hypotenuse. using the sides, find the distance between the two points in simplest radical form. (-3, -7) and (-7, -1) click twice to draw a line. click a segment to erase it. answer attempt 1 out of 2 leg 1: leg 2: hypotenuse: √ submit answer

Explanation:

Step1: Identify coordinates

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

Step2: Calculate horizontal leg

Horizontal difference: \(|x_1 - x_2| = |-3 - (-7)| = |4| = 4\).

Step3: Calculate vertical leg

Vertical difference: \(|y_1 - y_2| = |-7 - (-1)| = |-6| = 6\).

Step4: Apply distance formula

Distance \(d = \sqrt{(x_1 - x_2)^2 + (y_1 - y_2)^2} = \sqrt{4^2 + 6^2}\).

Step5: Simplify the radical

\(\sqrt{16 + 36} = \sqrt{52} = \sqrt{4\times13} = 2\sqrt{13}\).

Answer:

\(2\sqrt{13}\)