Question

find the distance between the points (6,4) and (-3,-8).
round decimals to the nearest tenth.

Explanation:

Step1: Identify the coordinates

Let \((x_1,y_1)=(6,4)\) and \((x_2,y_2)=(-3,-8)\)

Step2: Use the distance formula

The distance formula is \(d = \sqrt{(x_2 - x_1)^2+(y_2 - y_1)^2}\)
Substitute the values: \(d=\sqrt{(-3 - 6)^2+(-8 - 4)^2}\)

Step3: Calculate the differences

\(-3-6=-9\) and \(-8 - 4=-12\)
So \(d=\sqrt{(-9)^2+(-12)^2}\)

Step4: Square the differences

\((-9)^2 = 81\) and \((-12)^2=144\)
Then \(d=\sqrt{81 + 144}\)

Step5: Add the values inside the square - root

\(81+144 = 225\)
So \(d=\sqrt{225}\)

Step6: Find the square - root

\(\sqrt{225}=15\)

Answer:

\(15\)