Question

apply the pythagorean theorem to find the length between (-1,6) and (5, -2). round your answer to the nearest hundredth, if necessary. (1 point)

100

14

10

9 22

Explanation:

Step1: Calculate the horizontal and vertical distances

The horizontal distance \( \Delta x=5 - (-1)=6\).
The vertical distance \( \Delta y=-2 - 6=-8\).

Step2: Apply the Pythagorean Theorem

The distance \(d\) between two points \((x_1,y_1)\) and \((x_2,y_2)\) is given by \(d=\sqrt{(\Delta x)^2+(\Delta y)^2}\).
Substitute \(\Delta x = 6\) and \(\Delta y=-8\) into the formula: \(d=\sqrt{6^{2}+(-8)^{2}}=\sqrt{36 + 64}=\sqrt{100}\).

Step3: Simplify the result

\(\sqrt{100}=10\).

Answer:

10