distance formula quiz
problems: find the distance between each pair of points. round to the nearest tenth.
1. (-2, 1) (3, 3)
2. (0, 0) (4, 3)
3. (5, -3) (1, -7)
4. (-6, -2) (4, 1)
5. (1, 5) (6, 1)
6. (-4, 1) (1, 0)
7. (-1, 3) (3, 3)
8. (-2, -4) (-2, 7)
9. (0, 0) (7, 7)
10. (-5, -3) (-1, 5)
11. (-8, -3) (6, -3)
12. (6, 6) (12, 13)

Question

Accepted Answer

Let's solve each problem using the distance formula $ d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2} $.

### Problem 1: $(-2, 1)$ and $(3, 3)$
## Step 1: Identify coordinates
$ x_1 = -2, y_1 = 1, x_2 = 3, y_2 = 3 $
## Step 2: Apply distance formula
$ d = \sqrt{(3 - (-2))^2 + (3 - 1)^2} = \sqrt{(5)^2 + (2)^2} = \sqrt{25 + 4} = \sqrt{29} \approx 5.39 $
# Answer: $ \sqrt{29} $ (or approximately 5.39)

### Problem 2: $(0, 0)$ and $(4, 3)$
## Step 1: Identify coordinates
$ x_1 = 0, y_1 = 0, x_2 = 4, y_2 = 3 $
## Step 2: Apply distance formula
$ d = \sqrt{(4 - 0)^2 + (3 - 0)^2} = \sqrt{16 + 9} = \sqrt{25} = 5 $
# Answer: 5

### Problem 3: $(5, -3)$ and $(1, -7)$
## Step 1: Identify coordinates
$ x_1 = 5, y_1 = -3, x_2 = 1, y_2 = -7 $
## Step 2: Apply distance formula
$ d = \sqrt{(1 - 5)^2 + (-7 - (-3))^2} = \sqrt{(-4)^2 + (-4)^2} = \sqrt{16 + 16} = \sqrt{32} = 4\sqrt{2} \approx 5.66 $
# Answer: $ 4\sqrt{2} $ (or approximately 5.66)

### Problem 4: $(-6, -2)$ and $(4, 1)$
## Step 1: Identify coordinates
$ x_1 = -6, y_1 = -2, x_2 = 4, y_2 = 1 $
## Step 2: Apply distance formula
$ d = \sqrt{(4 - (-6))^2 + (1 - (-2))^2} = \sqrt{(10)^2 + (3)^2} = \sqrt{100 + 9} = \sqrt{109} \approx 10.44 $
# Answer: $ \sqrt{109} $ (or approximately 10.44)

### Problem 5: $(1, 5)$ and $(6, 1)$
## Step 1: Identify coordinates
$ x_1 = 1, y_1 = 5, x_2 = 6, y_2 = 1 $
## Step 2: Apply distance formula
$ d = \sqrt{(6 - 1)^2 + (1 - 5)^2} = \sqrt{(5)^2 + (-4)^2} = \sqrt{25 + 16} = \sqrt{41} \approx 6.40 $
# Answer: $ \sqrt{41} $ (or approximately 6.40)

### Problem 6: $(-4, 1)$ and $(1, 0)$
## Step 1: Identify coordinates
$ x_1 = -4, y_1 = 1, x_2 = 1, y_2 = 0 $
## Step 2: Apply distance formula
$ d = \sqrt{(1 - (-4))^2 + (0 - 1)^2} = \sqrt{(5)^2 + (-1)^2} = \sqrt{25 + 1} = \sqrt{26} \approx 5.10 $
# Answer: $ \sqrt{26} $ (or approximately 5.10)

### Problem 7: $(-1, 3)$ and $(3, 3)$
## Step 1: Identify coordinates
$ x_1 = -1, y_1 = 3, x_2 = 3, y_2 = 3 $
## Step 2: Apply distance formula
$ d = \sqrt{(3 - (-1))^2 + (3 - 3)^2} = \sqrt{(4)^2 + (0)^2} = \sqrt{16 + 0} = 4 $
# Answer: 4

### Problem 8: $(-2, -4)$ and $(-2, 7)$
## Step 1: Identify coordinates
$ x_1 = -2, y_1 = -4, x_2 = -2, y_2 = 7 $
## Step 2: Apply distance formula
$ d = \sqrt{(-2 - (-2))^2 + (7 - (-4))^2} = \sqrt{(0)^2 + (11)^2} = \sqrt{0 + 121} = 11 $
# Answer: 11

### Problem 9: $(0, 0)$ and $(7, 7)$
## Step 1: Identify coordinates
$ x_1 = 0, y_1 = 0, x_2 = 7, y_2 = 7 $
## Step 2: Apply distance formula
$ d = \sqrt{(7 - 0)^2 + (7 - 0)^2} = \sqrt{(7)^2 + (7)^2} = \sqrt{49 + 49} = \sqrt{98} = 7\sqrt{2} \approx 9.899 $
# Answer: $ 7\sqrt{2} $ (or approximately 9.90)

### Problem 10: $(-5, -3)$ and $(-1, 5)$
## Step 1: Identify coordinates
$ x_1 = -5, y_1 = -3, x_2 = -1, y_2 = 5 $
## Step 2: Apply distance formula
$ d = \sqrt{(-1 - (-5))^2 + (5 - (-3))^2} = \sqrt{(4)^2 + (8)^2} = \sqrt{16 + 64} = \sqrt{80} = 4\sqrt{5} \approx 8.944 $
# Answer: $ 4\sqrt{5} $ (or approximately 8.94)

### Problem 11: $(-8, -3)$ and $(6, -3)$
## Step 1: Identify coordinates
$ x_1 = -8, y_1 = -3, x_2 = 6, y_2 = -3 $
## Step 2: Apply distance formula
$ d = \sqrt{(6 - (-8))^2 + (-3 - (-3))^2} = \sqrt{(14)^2 + (0)^2} = \sqrt{196 + 0} = 14 $
# Answer: 14

### Problem 12: $(6, 6)$ and $(12, 13)$
## Step 1: Identify coordinates
$ x_1 = 6, y_1 = 6, x_2 = 12, y_2 = 13 $
## Step 2: Apply distance formula
$ d = \sqrt{(12 - 6)^2 + (13 - 6)^2} = \sqrt{(6)^2 + (7)^2} = \sqrt{36 + 49} = \sqrt{85} \approx 9.2195 $
# Answer: $ \sqrt{85} $ (or approximately 9.22)

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QUESTION IMAGE

Question

Explanation:

Problem 1: \((-2, 1)\) and \((3, 3)\)

Step 1: Identify coordinates

Step 2: Apply distance formula

Answer:

Problem 2: \((0, 0)\) and \((4, 3)\)

Step 1: Identify coordinates

Step 2: Apply distance formula