Question

use the pythagorean theorem to find the length of the segment with endpoints s(-1,2) and t(3, -2). (check out example 1 from the pythagorean theorem and distance formula lesson.) possible points: 10

Explanation:

Step1: Find horizontal distance

The horizontal distance $d_x$ between the points $S(-1,2)$ and $T(3, - 2)$ is the difference in $x$-coordinates. $d_x=\vert3 - (-1)\vert=\vert3 + 1\vert = 4$.

Step2: Find vertical distance

The vertical distance $d_y$ between the points is the difference in $y$-coordinates. $d_y=\vert-2 - 2\vert=\vert-4\vert = 4$.

Step3: Apply Pythagorean theorem

The length $d$ of the line - segment between the two points is given by $d=\sqrt{d_x^{2}+d_y^{2}}$. Substitute $d_x = 4$ and $d_y = 4$ into the formula: $d=\sqrt{4^{2}+4^{2}}=\sqrt{16 + 16}=\sqrt{32}\approx5.66$.

Answer:

5.66