Question

answer the following: * 13 a: (5,7) b: (-3,1) 14 a: (-4,2) b: (2,-2) 15 a: (0,-5) b: (4,2) 16 a: (3,-3) b: (-3,0) 17 a: (-1,-2) b: (-3,2) 18 a: (0,-4) m: (-4,0) find the distance between points a and b. answer in simplest radical form: 6.7 a 10 b 7.2 c 8.1 d 4.5 e 20.1 f 6.3 g 12.6 h 5.7 i

Explanation:

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

Problem 13: A(5,7) and B(-3,1)

Step 1: Identify coordinates

\( x_1 = 5, y_1 = 7, x_2 = -3, y_2 = 1 \)

Step 2: Apply distance formula

\( d = \sqrt{(-3 - 5)^2 + (1 - 7)^2} = \sqrt{(-8)^2 + (-6)^2} = \sqrt{64 + 36} = \sqrt{100} = 10 \)

Problem 14: A(-4,2) and B(2,-2)

Step 1: Identify coordinates

\( x_1 = -4, y_1 = 2, x_2 = 2, y_2 = -2 \)

Step 2: Apply distance formula

\( d = \sqrt{(2 - (-4))^2 + (-2 - 2)^2} = \sqrt{(6)^2 + (-4)^2} = \sqrt{36 + 16} = \sqrt{52} = 2\sqrt{13} \approx 7.2 \)

Problem 15: A(0,-5) and B(4,2)

Step 1: Identify coordinates

\( x_1 = 0, y_1 = -5, x_2 = 4, y_2 = 2 \)

Step 2: Apply distance formula

\( d = \sqrt{(4 - 0)^2 + (2 - (-5))^2} = \sqrt{(4)^2 + (7)^2} = \sqrt{16 + 49} = \sqrt{65} \approx 8.1 \)

Problem 16: A(3,-3) and B(-3,0)

Step 1: Identify coordinates

\( x_1 = 3, y_1 = -3, x_2 = -3, y_2 = 0 \)

Step 2: Apply distance formula

\( d = \sqrt{(-3 - 3)^2 + (0 - (-3))^2} = \sqrt{(-6)^2 + (3)^2} = \sqrt{36 + 9} = \sqrt{45} = 3\sqrt{5} \approx 6.7 \)

Problem 17: A(-1,-2) and B(-3,2)

Step 1: Identify coordinates

\( x_1 = -1, y_1 = -2, x_2 = -3, y_2 = 2 \)

Step 2: Apply distance formula

\( d = \sqrt{(-3 - (-1))^2 + (2 - (-2))^2} = \sqrt{(-2)^2 + (4)^2} = \sqrt{4 + 16} = \sqrt{20} = 2\sqrt{5} \approx 4.5 \)

Problem 18: A(0,-4) and M(-4,0)

Step 1: Identify coordinates

\( x_1 = 0, y_1 = -4, x_2 = -4, y_2 = 0 \)

Step 2: Apply distance formula

\( d = \sqrt{(-4 - 0)^2 + (0 - (-4))^2} = \sqrt{(-4)^2 + (4)^2} = \sqrt{16 + 16} = \sqrt{32} = 4\sqrt{2} \approx 5.7 \)

Answer:

s:

1. B (10)
2. C (7.2)
3. D (8.1)
4. A (6.7)
5. E (4.5)
6. I (5.7)