Question

apply the pythagorean theorem to find the length between (0,6) and (-3,-2). round your answer to the nearest hundredth, if necessary. (1 point) 73 8.54 6.08 11

Explanation:

Step1: Find the differences in coordinates

Let \((x_1,y_1)=(0,6)\) and \((x_2,y_2)=(-3,-2)\).
The difference in \(x\) - coordinates: \(\Delta x=x_2 - x_1=-3 - 0=-3\).
The difference in \(y\) - coordinates: \(\Delta y=y_2 - y_1=-2 - 6=-8\).

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

\(d=\sqrt{(-3)^2+(-8)^2}=\sqrt{9 + 64}=\sqrt{73}\approx8.54\)

Answer:

B. \(8.54\)