Question

1. the coordinates of a are (5, 2) and the coordinates of c are (3, −6). what is the distance between the two points?

a. -2
b. 8.2
c. 17
d. 4

Explanation:

Step1: Recall distance formula

The distance \( d \) between two points \((x_1, y_1)\) and \((x_2, y_2)\) is given by \( d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2} \).

Step2: Identify coordinates

Here, \( (x_1, y_1) = (5, 2) \) and \( (x_2, y_2) = (3, -6) \).

Step3: Substitute into formula

Calculate \( x_2 - x_1 = 3 - 5 = -2 \) and \( y_2 - y_1 = -6 - 2 = -8 \).
Then, \( d = \sqrt{(-2)^2 + (-8)^2} = \sqrt{4 + 64} = \sqrt{68} \approx 8.2 \).

Answer:

B. 8.2