Question

pythagorean distance
what is the horizontal distance a?
(there is a coordinate grid with points and a right triangle, and the pythagorean formula c² = a² + b² is shown. on the right, there are number and square root option buttons.)

Explanation:

Step1: Identify the x - coordinates of the two points

The left - most point (the blue ball on the left) is at \(x = 1\) (since it is on the vertical line corresponding to \(x = 1\) on the x - axis). The right - most point (the blue ball on the right, the end of the horizontal dashed line) is at \(x = 5\) (since it is on the vertical line corresponding to \(x = 5\) on the x - axis).

Step2: Calculate the horizontal distance \(a\)

The horizontal distance \(a\) between two points with x - coordinates \(x_1\) and \(x_2\) is given by \(|x_2 - x_1|\). Here, \(x_1=1\) and \(x_2 = 5\), so \(a=|5 - 1|=4\).

Answer:

\(4\)