Question

find the distance between the two points rounding to the nearest tenth (if necessary). (2,5) and (-6,-3)

Explanation:

Step1: Recall the distance formula

The distance \( d \) between two points \( (x_1, y_1) \) and \( (x_2, y_2) \) is given by \( d=\sqrt{(x_2 - x_1)^2+(y_2 - y_1)^2} \).
Here, \( x_1 = 2 \), \( y_1 = 5 \), \( x_2=-6 \), \( y_2 = - 3 \).

Step2: Substitute the values into the formula

First, calculate \( x_2 - x_1=-6 - 2=-8 \) and \( y_2 - y_1=-3 - 5=-8 \).
Then, substitute these into the formula: \( d=\sqrt{(-8)^2+(-8)^2} \).

Step3: Simplify the expression inside the square root

Calculate \( (-8)^2 = 64 \), so we have \( d=\sqrt{64 + 64}=\sqrt{128} \).

Step4: Simplify the square root and round

\( \sqrt{128}=\sqrt{64\times2}=8\sqrt{2}\approx8\times1.414 = 11.312 \). Rounding to the nearest tenth gives \( 11.3 \).

Answer:

\( 11.3 \)