Question

find the distance between each pair of points. round your answer to the nearest tenth, if necessary.

1. (7, 6), (0, 2)
2. (4, 2), (-6, -6)
3. (-6, 1), (-3, 1)
4. (-3, 6), (2, 1)

11)
12)
13)
14)

Explanation:

Identify the distance formula

To find the distance \(d\) between any two points \((x_1, y_1)\) and \((x_2, y_2)\) on a coordinate plane, we use the Distance Formula:

$$d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}$$

We will apply this formula to each pair of points, rounding to the nearest tenth when necessary.

Calculate distances for coordinate pairs (7 to 10)

• Question 7: Points \((7, 6)\) and \((0, 2)\)

$$d = \sqrt{(0 - 7)^2 + (2 - 6)^2} = \sqrt{(-7)^2 + (-4)^2} = \sqrt{49 + 16} = \sqrt{65} \approx 8.1$$

• Question 8: Points \((4, 2)\) and \((-6, -6)\)

$$d = \sqrt{(-6 - 4)^2 + (-6 - 2)^2} = \sqrt{(-10)^2 + (-8)^2} = \sqrt{100 + 64} = \sqrt{164} \approx 12.8$$

• Question 9: Points \((-6, 1)\) and \((-3, 1)\)

Since the \(y\)-coordinates are equal, the distance is the horizontal difference:

$$d = |-3 - (-6)| = |-3 + 6| = 3$$

• Question 10: Points \((-3, 6)\) and \((2, 1)\)

$$d = \sqrt{(2 - (-3))^2 + (1 - 6)^2} = \sqrt{(5)^2 + (-5)^2} = \sqrt{25 + 25} = \sqrt{50} \approx 7.1$$

Identify coordinates from graphs (11 to 14)

We read the endpoints of each segment from the grid:

• Question 11: Endpoints are \((-1, 4)\) and \((3, -1)\)
• Question 12: Endpoints are \((-4, 2)\) and \((5, -3)\)
• Question 13: Endpoints are \((0, -2)\) and \((1, -4)\)
• Question 14: Endpoints are \((-4, -3)\) and \((1, 0)\)

Calculate distances for graphed segments (11 to 14)

• Question 11: Points \((-1, 4)\) and \((3, -1)\)

$$d = \sqrt{(3 - (-1))^2 + (-1 - 4)^2} = \sqrt{4^2 + (-5)^2} = \sqrt{16 + 25} = \sqrt{41} \approx 6.4$$

• Question 12: Points \((-4, 2)\) and \((5, -3)\)

$$d = \sqrt{(5 - (-4))^2 + (-3 - 2)^2} = \sqrt{9^2 + (-5)^2} = \sqrt{81 + 25} = \sqrt{106} \approx 10.3$$

• Question 13: Points \((0, -2)\) and \((1, -4)\)

$$d = \sqrt{(1 - 0)^2 + (-4 - (-2))^2} = \sqrt{1^2 + (-2)^2} = \sqrt{1 + 4} = \sqrt{5} \approx 2.2$$

• Question 14: Points \((-4, -3)\) and \((1, 0)\)

$$d = \sqrt{(1 - (-4))^2 + (0 - (-3))^2} = \sqrt{5^2 + 3^2} = \sqrt{25 + 9} = \sqrt{34} \approx 5.8$$

Answer:

Question 7

\(8.1\)

Question 8

\(12.8\)

Question 9

\(3\)

Question 10

\(7.1\)

Question 11

\(6.4\)

Question 12

\(10.3\)

Question 13

\(2.2\)

Question 14

\(5.8\)