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.
$(3,6)$ and $(5,1)$
click twice to draw a line. click a segment to erase it.
answer
leg 1:
leg 2:
hypotenuse:

Explanation:

Step1: Find the length of horizontal leg

The horizontal distance between the \(x -\)coordinates of the points \((3,6)\) and \((5,1)\) is calculated as \(|x_2 - x_1|\). Here, \(x_1 = 3\) and \(x_2=5\), so \(|5 - 3|=2\).

Step2: Find the length of vertical leg

The vertical distance between the \(y -\)coordinates of the points \((3,6)\) and \((5,1)\) is calculated as \(|y_2 - y_1|\). Here, \(y_1 = 6\) and \(y_2 = 1\), so \(|1 - 6|=5\).

Step3: Use the Pythagorean theorem

The Pythagorean theorem is \(c=\sqrt{a^{2}+b^{2}}\), where \(a = 2\) (horizontal leg) and \(b = 5\) (vertical leg). Then \(c=\sqrt{2^{2}+5^{2}}=\sqrt{4 + 25}=\sqrt{29}\).

Answer:

Leg 1: \(2\), Leg 2: \(5\), Hypotenuse: \(\sqrt{29}\)