Question

using the distance formula
find the distance between the points. for decimal points, round to the nearest hundredth.

1. (4,2), (-6,-5)
2. (-1,5), (7,-2)
3. (2,9), (7,6)
4. (-9,3), (6,7)
5. (5,3), (-9,7)
6. (2,-6), (3,8)
7. (-8,3), (2,6)
8. (-4,1), (-6,-9)

Explanation:

Step1: Recall the distance formula

The distance formula between two points \((x_1,y_1)\) and \((x_2,y_2)\) is \(d = \sqrt{(x_2 - x_1)^2+(y_2 - y_1)^2}\)

Step2: Substitute the values for problem 8

For the points \((-4,1)\) and \((-6,-9)\), \(x_1=-4,y_1 = 1,x_2=-6,y_2=-9\)
\(d=\sqrt{(-6-(-4))^2+(-9 - 1)^2}=\sqrt{(-2)^2+(-10)^2}\)

Step3: Calculate the squares

\(\sqrt{4 + 100}=\sqrt{104}\)

Step4: Simplify the square - root

\(\sqrt{104}\approx10.20\) (rounded to the nearest hundredth)

Answer:

\(10.20\)