Question

apply the pythagorean theorem to find the length between (2,5) and (7,3). round your answer to the nearest hundredth, if necessary. (1 point)
29
2.65
4.58
5.39

Explanation:

Step1: Find the differences in x and y coordinates

Let \((x_1,y_1)=(2,5)\) and \((x_2,y_2)=(7,3)\).
The difference in x - coordinates: \(\Delta x=x_2 - x_1=7 - 2 = 5\)
The difference in y - coordinates: \(\Delta y=y_2 - y_1=3 - 5=- 2\)

Step2: Apply the Pythagorean theorem (distance formula \(d=\sqrt{(\Delta x)^2+(\Delta y)^2}\))

Substitute \(\Delta x = 5\) and \(\Delta y=-2\) into the formula:
\(d=\sqrt{(5)^2+(-2)^2}=\sqrt{25 + 4}=\sqrt{29}\approx5.39\)

Answer:

5.39