Question

draw a right triangle where st is the hypotenuse and the legs intersect at r. point r has coordinates of. the length of rs is < >, and the length of rt is < >. using the pythagorean theorem, the length of st is approximately < >. select the correct answer from each drop - down menu. explain how the distance of the line segment shown on the graph can be found.

Explanation:

Step1: Identify coordinates

Assume \(S(x_1,y_1)\) and \(T(x_2,y_2)\) from the graph. Let's say \(S(3, - 1)\) and \(T(5,-3)\). First, find the horizontal and vertical distances between the points for the right - triangle legs.
The horizontal distance (one leg \(RS\)) between \(S\) and \(T\) is \(|x_2 - x_1|=|5 - 3| = 2\).
The vertical distance (the other leg \(RT\)) between \(S\) and \(T\) is \(|y_2 - y_1|=|-3+1| = 2\).

Step2: Apply Pythagorean theorem

The Pythagorean theorem for a right - triangle is \(a^{2}+b^{2}=c^{2}\), where \(c\) is the hypotenuse (\(ST\)) and \(a\) and \(b\) are the legs. Here \(a = RS = 2\) and \(b = RT = 2\).
So, \(ST=\sqrt{RS^{2}+RT^{2}}=\sqrt{2^{2}+2^{2}}=\sqrt{4 + 4}=\sqrt{8}\approx2.83\).

Answer:

The length of \(RS\) is \(2\), the length of \(RT\) is \(2\), and the length of \(ST\) is approximately \(2.83\).