Question

graph a right triangle with the two points forming the hypotenuse. using the sides, find the distance between the two points in
$(1,-2)$ and $(4,2)$
click twice to draw a line. click a segment to erase it.

Explanation:

Step1: Calculate the horizontal leg length

The horizontal leg length is the difference in \(x -\)coordinates.
For points \((1,-2)\) and \((4,2)\), \(x_1 = 1,x_2=4\).
\(\vert x_2 - x_1\vert=\vert4 - 1\vert=3\)

Step2: Calculate the vertical leg length

The vertical leg length is the difference in \(y -\)coordinates.
For points \((1,-2)\) and \((4,2)\), \(y_1=-2,y_2 = 2\).
\(\vert y_2 - y_1\vert=\vert2-(-2)\vert=\vert2 + 2\vert=4\)

Step3: Use the Pythagorean theorem to find the hypotenuse (distance)

By the Pythagorean theorem \(c=\sqrt{a^{2}+b^{2}}\), where \(a = 3\), \(b = 4\).
\(c=\sqrt{3^{2}+4^{2}}=\sqrt{9 + 16}=\sqrt{25}=5\)

Answer:

Leg 1: \(3\), Leg 2: \(4\), Hypotenuse: \(5\)