Question

example: find the distance between the points (5, -1) and (3, 7). distance = \sqrt{(x_2 - x_1)^2+(y_2 - y_1)^2}=\sqrt{(3 - 5)^2+(7 + 1)^2}=\sqrt{(-2)^2+(8)^2}=\sqrt{4 + 64}=\sqrt{68}\approx8.25 units. find the distance between the points. round the answer to two decimal places. 1) (1, 3), (5, 7) 2) (-8, -9), (-4, -10) 3) (10, 6), (1, -4) 4) (3, 2), (8, 2) 5) (9, -3), (-1, 8) 6) (10, 0), (0, 4) 7) (-7, -2), (6, 9) 8) (-6, 5), (8, -3) 9) (-5, -6), (-9, -4) 10) (2, 0), (-7, 1)

Explanation:

Step1: Identify 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: Solve for each pair of points

1) For points $(1,3)$ and $(5,7)$

$x_1 = 1,y_1=3,x_2 = 5,y_2 = 7$
$d=\sqrt{(5 - 1)^2+(7 - 3)^2}=\sqrt{4^2+4^2}=\sqrt{16 + 16}=\sqrt{32}\approx5.66$

2) For points $(-8,-9)$ and $(-4,-10)$

$x_1=-8,y_1 = - 9,x_2=-4,y_2=-10$
$d=\sqrt{(-4+8)^2+(-10 + 9)^2}=\sqrt{4^2+(-1)^2}=\sqrt{16+1}=\sqrt{17}\approx4.12$

3) For points $(10,6)$ and $(1,-4)$

$x_1 = 10,y_1=6,x_2 = 1,y_2=-4$
$d=\sqrt{(1 - 10)^2+(-4 - 6)^2}=\sqrt{(-9)^2+(-10)^2}=\sqrt{81 + 100}=\sqrt{181}\approx13.45$

4) For points $(3,2)$ and $(8,2)$

$x_1 = 3,y_1=2,x_2 = 8,y_2=2$
$d=\sqrt{(8 - 3)^2+(2 - 2)^2}=\sqrt{5^2+0^2}=5.00$

5) For points $(9,-3)$ and $(-1,8)$

$x_1 = 9,y_1=-3,x_2=-1,y_2 = 8$
$d=\sqrt{(-1 - 9)^2+(8 + 3)^2}=\sqrt{(-10)^2+11^2}=\sqrt{100+121}=\sqrt{221}\approx14.87$

6) For points $(10,0)$ and $(0,4)$

$x_1 = 10,y_1=0,x_2 = 0,y_2=4$
$d=\sqrt{(0 - 10)^2+(4 - 0)^2}=\sqrt{(-10)^2+4^2}=\sqrt{100 + 16}=\sqrt{116}\approx10.77$

7) For points $(-7,-2)$ and $(6,9)$

$x_1=-7,y_1=-2,x_2 = 6,y_2=9$
$d=\sqrt{(6 + 7)^2+(9 + 2)^2}=\sqrt{13^2+11^2}=\sqrt{169+121}=\sqrt{290}\approx17.03$

8) For points $(-6,5)$ and $(8,-3)$

$x_1=-6,y_1=5,x_2 = 8,y_2=-3$
$d=\sqrt{(8 + 6)^2+(-3 - 5)^2}=\sqrt{14^2+(-8)^2}=\sqrt{196+64}=\sqrt{260}\approx16.12$

9) For points $(-5,-6)$ and $(-9,-4)$

$x_1=-5,y_1=-6,x_2=-9,y_2=-4$
$d=\sqrt{(-9 + 5)^2+(-4 + 6)^2}=\sqrt{(-4)^2+2^2}=\sqrt{16 + 4}=\sqrt{20}\approx4.47$

10) For points $(2,0)$ and $(-7,1)$

$x_1 = 2,y_1=0,x_2=-7,y_2=1$
$d=\sqrt{(-7 - 2)^2+(1 - 0)^2}=\sqrt{(-9)^2+1^2}=\sqrt{81+1}=\sqrt{82}\approx9.06$

Answer:

1. $5.66$
2. $4.12$
3. $13.45$
4. $5.00$
5. $14.87$
6. $10.77$
7. $17.03$
8. $16.12$
9. $4.47$
10. $9.06$