Question

find the distance between the points (1, 3) and (-2, 6).
a 2
b 2√5
c 6
d 3√2

Explanation:

Step1: Recall the 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 the coordinates

Here, \( (x_1, y_1) = (1, 3) \) and \( (x_2, y_2) = (-2, 6) \).

Step3: Substitute into the formula

First, calculate the differences in coordinates: \( x_2 - x_1 = -2 - 1 = -3 \) and \( y_2 - y_1 = 6 - 3 = 3 \).
Then, substitute these into the distance formula: \( d = \sqrt{(-3)^2 + 3^2} \).

Step4: Simplify the expression

Calculate the squares: \( (-3)^2 = 9 \) and \( 3^2 = 9 \). Then, \( d = \sqrt{9 + 9} = \sqrt{18} \). Simplify \( \sqrt{18} \) as \( \sqrt{9 \times 2} = 3\sqrt{2} \).

Answer:

D. \( 3\sqrt{2} \)