Question

distance formula
l151
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 coordinates

For problem 1: \((x_1,y_1)=(1,3)\), \((x_2,y_2)=(5,7)\)

Step2: Substitute into distance formula

$$
LATEXBLOCK0
$$

Step3: For problem 2: \((x_1,y_1)=(-8,-9)\), \((x_2,y_2)=(-4,-10)\)

$$
LATEXBLOCK1
$$

Step4: For problem 3: \((x_1,y_1)=(10,6)\), \((x_2,y_2)=(1,-4)\)

$$
LATEXBLOCK2
$$

Step5: For problem 4: \((x_1,y_1)=(3,2)\), \((x_2,y_2)=(8,2)\)

$$
LATEXBLOCK3
$$

Step6: For problem 5: \((x_1,y_1)=(9,-3)\), \((x_2,y_2)=(-1,8)\)

$$
LATEXBLOCK4
$$

Step7: For problem 6: \((x_1,y_1)=(10,0)\), \((x_2,y_2)=(0,4)\)

$$
LATEXBLOCK5
$$

Step8: For problem 7: \((x_1,y_1)=(-7,-2)\), \((x_2,y_2)=(6,9)\)

$$
LATEXBLOCK6
$$

Step9: For problem 8: \((x_1,y_1)=(-6,5)\), \((x_2,y_2)=(8,-3)\)

$$
LATEXBLOCK7
$$

Step10: For problem 9: \((x_1,y_1)=(-5,-6)\), \((x_2,y_2)=(-9,-4)\)

$$
LATEXBLOCK8
$$

Step11: For problem 10: \((x_1,y_1)=(2,0)\), \((x_2,y_2)=(-7,1)\)

$$
LATEXBLOCK9
$$

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. \(9.06\)