Question

pythagorean distance
what is the vertical distance b?
(there is a coordinate grid with two blue dots, a line segment c, horizontal distance a=4, and vertical distance b=? the pythagorean formula c² = a² + b² is shown. on the right, there are number and square root option buttons.)

Explanation:

Step1: Identify vertical coordinates

The top point has y - coordinate 4, the bottom point has y - coordinate 1.

Step2: Calculate vertical distance

Vertical distance \( b \) is the difference in y - coordinates: \( b=4 - 1=3 \)? Wait, no, wait. Wait, the top point is at (5,4), bottom at (5,1). So vertical distance is \( 4 - 1 = 3 \)? But wait, maybe I misread. Wait, the horizontal distance \( a = 4 \) (from x = 1 to x = 5, \( 5-1 = 4 \)). The vertical distance: the top point's y is 4, bottom's y is 1. So \( b=4 - 1=3 \). Wait, but let's check. The vertical line is from y = 1 to y = 4, so the length is \( 4 - 1=3 \).

Wait, maybe I made a mistake. Wait, the two points: one at (1,1), one at (5,4). So horizontal change (a) is \( 5 - 1=4 \), vertical change (b) is \( 4 - 1 = 3 \). So \( b = 3 \).

Answer:

3