Question

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

1. (4,2), (-6,-5)

12.20

1. (2,9), (7,6)

5.83

1. (5,3), (-9,7)

14.56

1. (-8,3), (2,6)

10.44

1. (-1,5), (7,-2)

10.63

1. (-9,3), (6,7)

16.52

1. (2,-6), (3,8)

14.04

1. (-4,1), (-6,-9)

10.20

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: Calculate for problem 1

For the points \((4,2)\) and \((-6,-5)\), \(x_1 = 4,y_1=2,x_2=-6,y_2 = -5\).
\(d=\sqrt{(-6 - 4)^2+(-5 - 2)^2}=\sqrt{(-10)^2+(-7)^2}=\sqrt{100 + 49}=\sqrt{149}\approx12.20\)

Step3: Calculate for problem 2

For the points \((2,9)\) and \((7,6)\), \(x_1 = 2,y_1=9,x_2=7,y_2 = 6\).
\(d=\sqrt{(7 - 2)^2+(6 - 9)^2}=\sqrt{5^2+(-3)^2}=\sqrt{25+9}=\sqrt{34}\approx5.83\)

Step4: Calculate for problem 3

For the points \((5,3)\) and \((-9,7)\), \(x_1 = 5,y_1=3,x_2=-9,y_2 = 7\).
\(d=\sqrt{(-9 - 5)^2+(7 - 3)^2}=\sqrt{(-14)^2+4^2}=\sqrt{196 + 16}=\sqrt{212}\approx14.56\)

Step5: Calculate for problem 4

For the points \((-8,3)\) and \((2,6)\), \(x_1=-8,y_1 = 3,x_2=2,y_2=6\).
\(d=\sqrt{(2+8)^2+(6 - 3)^2}=\sqrt{10^2+3^2}=\sqrt{100+9}=\sqrt{109}\approx10.44\)

Step6: Calculate for problem 5

For the points \((-1,5)\) and \((7,-2)\), \(x_1=-1,y_1 = 5,x_2=7,y_2=-2\).
\(d=\sqrt{(7 + 1)^2+(-2 - 5)^2}=\sqrt{8^2+(-7)^2}=\sqrt{64 + 49}=\sqrt{113}\approx10.63\)

Step7: Calculate for problem 6

For the points \((-9,3)\) and \((6,7)\), \(x_1=-9,y_1 = 3,x_2=6,y_2=7\).
\(d=\sqrt{(6 + 9)^2+(7 - 3)^2}=\sqrt{15^2+4^2}=\sqrt{225+16}=\sqrt{241}\approx15.52\)

Step8: Calculate for problem 7

For the points \((2,-6)\) and \((3,8)\), \(x_1=2,y_1=-6,x_2=3,y_2 = 8\).
\(d=\sqrt{(3 - 2)^2+(8 + 6)^2}=\sqrt{1^2+14^2}=\sqrt{1+196}=\sqrt{197}\approx14.04\)

Step9: Calculate for problem 8

For the points \((-4,1)\) and \((-6,-9)\), \(x_1=-4,y_1 = 1,x_2=-6,y_2=-9\).
\(d=\sqrt{(-6 + 4)^2+(-9 - 1)^2}=\sqrt{(-2)^2+(-10)^2}=\sqrt{4 + 100}=\sqrt{104}\approx10.20\)

Answer:

1. \(12.20\)
2. \(5.83\)
3. \(14.56\)
4. \(10.44\)
5. \(10.63\)
6. \(15.52\)
7. \(14.04\)
8. \(10.20\)