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.
(-4,8) and (-6,6)
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: Find the lengths of the legs

For the horizontal leg (Leg 1), calculate the difference in the x - coordinates of the points \((-4,8)\) and \((-6,6)\). The formula for the length of a horizontal segment between two points \((x_1,y_1)\) and \((x_2,y_2)\) (where \(y_1 = y_2\)) is \(|x_1 - x_2|\). Here, \(x_1=-4\) and \(x_2 = - 6\), so \(| - 4-(-6)|=| - 4 + 6|=|2| = 2\).

For the vertical leg (Leg 2), calculate the difference in the y - coordinates of the points \((-4,8)\) and \((-6,6)\). The formula for the length of a vertical segment between two points \((x_1,y_1)\) and \((x_2,y_2)\) (where \(x_1=x_2\)) is \(|y_1 - y_2|\). Here, \(y_1 = 8\) and \(y_2=6\), so \(|8 - 6|=|2| = 2\).

Step2: Find the length of the hypotenuse

We use the Pythagorean theorem, which states that for a right triangle with legs of length \(a\) and \(b\) and hypotenuse of length \(c\), \(c=\sqrt{a^{2}+b^{2}}\). Here, \(a = 2\) and \(b = 2\), so \(c=\sqrt{2^{2}+2^{2}}=\sqrt{4 + 4}=\sqrt{8}=\sqrt{4\times2}=2\sqrt{2}\).

Answer:

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