Question

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

Explanation:

Step1: Determine point R

To form a right - triangle with $\overline{ST}$ as hypotenuse, we need to find a point R such that the legs are vertical and horizontal. By visual inspection, if we want to create right - angled segments from S and T, the point R with coordinates (- 2,3) will work.

Step2: Calculate length of $\overline{RS}$

Count the vertical distance from R(-2,3) to S. Let the coordinates of S be (-2,2). The length of $\overline{RS}=\vert3 - 2\vert=1$.

Step3: Calculate length of $\overline{RT}$

Count the horizontal distance from R(-2,3) to T. Let the coordinates of T be (1,3). The length of $\overline{RT}=\vert1-(-2)\vert = 3$.

Step4: Apply Pythagorean theorem

The Pythagorean theorem for a right - triangle is $c=\sqrt{a^{2}+b^{2}}$, where c is the hypotenuse and a, b are the legs. Here, $a = 1$, $b = 3$, so $c=\sqrt{1^{2}+3^{2}}=\sqrt{1 + 9}=\sqrt{10}\approx3.16$.

Answer:

Point R has coordinates of R(-2,3).
The length of $\overline{RS}$ is 1.
The length of $\overline{RT}$ is 3.
Using the Pythagorean theorem, the length of $\overline{ST}$ is approximately 3.16.