Question

skillstream: determining the distance between two points using the pythagorean theorem; 20 coins

type the answer in the space provided. use numbers instead of words.

calculate the distance between the two points on the coordinate plane.

Explanation:

Step1: Identify the coordinates

Let the first point be $(3,3)$ and the second point be $(6,7)$.

Step2: Find the horizontal and vertical distances

The horizontal distance $a=\vert6 - 3\vert=3$, and the vertical distance $b=\vert7 - 3\vert = 4$.

Step3: Apply the Pythagorean theorem

The distance $d$ between two points is given by $d=\sqrt{a^{2}+b^{2}}$. Substitute $a = 3$ and $b = 4$ into the formula: $d=\sqrt{3^{2}+4^{2}}=\sqrt{9 + 16}=\sqrt{25}=5$.

Answer:

5