Question

1. find the distance between each pair of points below:

a. (-3, 6) and (3, -2)
b. (-4, 4) and (5, 1)

1. find ac
2. find ac

Explanation:

1a. Step1: Identify coordinates

Let \((x_1, y_1) = (-3, 6)\), \((x_2, y_2) = (3, -2)\)

1a. Step2: Calculate differences

\(\Delta x = 3 - (-3) = 6\), \(\Delta y = -2 - 6 = -8\)

1a. Step3: Apply distance formula

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

1b. Step1: Identify coordinates

Let \((x_1, y_1) = (-4, 4)\), \((x_2, y_2) = (5, 1)\)

1b. Step2: Calculate differences

\(\Delta x = 5 - (-4) = 9\), \(\Delta y = 1 - 4 = -3\)

1b. Step3: Apply distance formula

\(d = \sqrt{9^2 + (-3)^2} = \sqrt{81 + 9} = \sqrt{90} = 3\sqrt{10}\)

Answer:

1a. 10
1b. \(3\sqrt{10}\)