Question

question
find the distance between the two points rounding to the nearest tenth (if necessary).
$(2,-3)$ and $(8,-7)$

Explanation:

Step1: Identify the coordinates

Let \((x_1,y_1)=(2,-3)\) and \((x_2,y_2)=(8,-7)\)

Step2: Use the distance formula

The distance formula is \(d = \sqrt{(x_2 - x_1)^2+(y_2 - y_1)^2}\)
Substitute the values: \(d=\sqrt{(8 - 2)^2+(-7+ 3)^2}\)

Step3: Calculate the differences

\(8 - 2=6\) and \(-7+3=-4\)
So \(d=\sqrt{6^2+(-4)^2}\)

Step4: Square the differences

\(6^2 = 36\) and \((-4)^2=16\)
Then \(d=\sqrt{36 + 16}=\sqrt{52}\)

Step5: Simplify the square root

\(\sqrt{52}=\sqrt{4\times13}=2\sqrt{13}\approx7.2\)

Answer:

\(7.2\)