Question

skillstream: determining the distance between two points using the pythagorean theorem : 30 coins

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

what is the distance between the two points on the coordinate plane? round your answer to the nearest tenth.

Explanation:

Step1: Identify the coordinates

Let the first - point be $(2,3)$ and the second - point be $(8,7)$.

Step2: Calculate the differences in x and y coordinates

The difference in x - coordinates $\Delta x=8 - 2=6$, and the difference in y - coordinates $\Delta y=7 - 3=4$.

Step3: Apply the distance formula (derived from Pythagorean theorem)

The distance $d=\sqrt{(\Delta x)^2+(\Delta y)^2}=\sqrt{6^{2}+4^{2}}=\sqrt{36 + 16}=\sqrt{52}$.

Step4: Simplify and round

$\sqrt{52}\approx7.2$

Answer:

7.2