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 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.

Explanation:

Step1: Determine coordinates of S and T

Assume S(-2, 3) and T(1, 5). For point R, we draw a right - triangle such that the vertical and horizontal lines from S and T meet at R. The x - coordinate of R is the same as that of S (-2) and the y - coordinate of R is the same as that of T(5). So R has coordinates (-2, 5).

Step2: Calculate lengths of RS and RT

The length of RS is the difference in y - coordinates of R and S. $RS=\vert5 - 3\vert= 2$. The length of RT is the difference in x - coordinates of T and R. $RT=\vert1-(-2)\vert = 3$.

Step3: Apply Pythagorean theorem

The Pythagorean theorem states that for a right - triangle with legs a and b and hypotenuse c, $c=\sqrt{a^{2}+b^{2}}$. Here, $a = 2$ and $b = 3$, so $ST=\sqrt{2^{2}+3^{2}}=\sqrt{4 + 9}=\sqrt{13}\approx3.61$.

Answer:

Point R has coordinates (-2, 5). The length of RS is 2, and the length of RT is 3. The length of ST is approximately 3.61.