Question

find the distance between the two points rounding to the nearest tenth (if necessary). (1, 4) and (-2, 8)

Explanation:

Step1: Recall Distance Formula

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

Step2: Identify Coordinates

Let \( (x_1, y_1) = (1, 4) \) and \( (x_2, y_2) = (-2, 8) \).

Step3: Substitute into Formula

Calculate \( x_2 - x_1 = -2 - 1 = -3 \) and \( y_2 - y_1 = 8 - 4 = 4 \). Then \( d = \sqrt{(-3)^2 + 4^2} \).

Step4: Simplify

\( (-3)^2 = 9 \), \( 4^2 = 16 \), so \( d = \sqrt{9 + 16} = \sqrt{25} = 5 \)? Wait, no: \( 9 + 16 = 25 \)? Wait, \( (-3)^2 = 9 \), \( 4^2 = 16 \), sum is \( 25 \), square root of \( 25 \) is \( 5 \). Wait, but let's check again. Wait, \( x_2 - x_1 = -2 - 1 = -3 \), squared is \( 9 \). \( y_2 - y_1 = 8 - 4 = 4 \), squared is \( 16 \). Sum is \( 25 \), square root is \( 5 \). Wait, but maybe I made a mistake? Wait, no, \( (-3)^2 = 9 \), \( 4^2 = 16 \), 9 + 16 = 25, square root of 25 is 5. So the distance is 5.

Answer:

5