Distance Formula Practice Worksheet with 10 problems and multiple-choice answers.

Here are the step-by-step solutions for the problems on your worksheet.

The Distance Formula is:
$$d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}$$

This basically means: find the difference in $x$, square it, add it to the squared difference in $y$, and then take the square root of the total.

Question 1

Points: $(3, -2)$ and $(-5, -8)$

1. Find the change in $x$: $3 - (-5) = 3 + 5 = 8$
2. Square it: $8^2 = 64$
3. Find the change in $y$: $-2 - (-8) = -2 + 8 = 6$
4. Square it: $6^2 = 36$
5. Add them together: $64 + 36 = 100$
6. Take the square root: $\sqrt{100} = 10$

Answer: 10

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Question 2

Points: $(8, 8)$ and $(3, -4)$

1. Change in $x$: $8 - 3 = 5$
2. Square it: $5^2 = 25$
3. Change in $y$: $8 - (-4) = 8 + 4 = 12$
4. Square it: $12^2 = 144$
5. Add them: $25 + 144 = 169$
6. Square root: $\sqrt{169} = 13$

Answer: 13

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Question 3

Points: $(-7, 5)$ and $(2, -7)$

1. Change in $x$: $-7 - 2 = -9$
2. Square it: $(-9)^2 = 81$
3. Change in $y$: $5 - (-7) = 5 + 7 = 12$
4. Square it: $12^2 = 144$
5. Add them: $81 + 144 = 225$
6. Square root: $\sqrt{225} = 15$

Answer: 15

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Question 4

Points: $(2, 1)$ and $(5, 5)$

1. Change in $x$: $2 - 5 = -3$
2. Square it: $(-3)^2 = 9$
3. Change in $y$: $1 - 5 = -4$
4. Square it: $(-4)^2 = 16$
5. Add them: $9 + 16 = 25$
6. Square root: $\sqrt{25} = 5$

Answer: 5

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Question 5

Points: $(-6, -3)$ and $(-4, -8)$

1. Change in $x$: $-6 - (-4) = -6 + 4 = -2$
2. Square it: $(-2)^2 = 4$
3. Change in $y$: $-3 - (-8) = -3 + 8 = 5$
4. Square it: $5^2 = 25$
5. Add them: $4 + 25 = 29$
6. Square root: $\sqrt{29} \approx 5.385...$

Rounding to one decimal place gives 5.4. Looking at the options provided:
A) 4.8
B) 5.3
C) 7.1
D) 6.6

*Note: The exact answer is approximately 5.4. Option B (5.3) is the closest value listed, though slightly inaccurate due to rounding or a typo in the question's options.*

Best Answer from options: B (5.3)

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Question 6

Points: $(8, -8)$ and $(3, -4)$

1. Change in $x$: $8 - 3 = 5$
2. Square it: $5^2 = 25$
3. Change in $y$: $-8 - (-4) = -8 + 4 = -4$
4. Square it: $(-4)^2 = 16$
5. Add them: $25 + 16 = 41$
6. Square root: $\sqrt{41} \approx 6.403...$

Looking at the options:
A) 3.2
B) 10
C) 6.4
D) 8.7

Answer: C (6.4)

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Question 7

Points: $(1, 5)$ and $(3, 8)$

1. Change in $x$: $1 - 3 = -2$
2. Square it: $(-2)^2 = 4$
3. Change in $y$: $5 - 8 = -3$
4. Square it: $(-3)^2 = 9$
5. Add them: $4 + 9 = 13$
6. Square root: $\sqrt{13} \approx 3.605...$

Looking at the options:
A) 7
B) 5.4
C) 2.2
D) 3.6

Answer: D (3.6)

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Question 8

Points: $(3, 7)$ and $(-5, -8)$

1. Change in $x$: $3 - (-5) = 3 + 5 = 8$
2. Square it: $8^2 = 64$
3. Change in $y$: $7 - (-8) = 7 + 8 = 15$
4. Square it: $15^2 = 225$
5. Add them: $64 + 225 = 289$
6. Square root: $\sqrt{289} = 17$

Answer: 17

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Final Answer:
1. 10
2. 13
3. 15
4. 5
5. B (5.3)
6. C (6.4)
7. D (3.6)
8. 17