Question

pythagorean distance
what is the vertical distance b?
pythagorean formula c² = a² + b²

Explanation:

Step1: Identify vertical distance

The vertical distance \( b \) is the difference in the \( y \)-coordinates of the two points. The lower point is at \( y = 3 \), the upper at \( y = 4 \).

Step2: Calculate \( b \)

\( b = 4 - 3 = 1 \)? Wait, no, wait. Wait, the horizontal distance \( a = 1 \) (from \( x = 2 \) to \( x = 3 \)). Wait, the vertical distance: the lower point is at \( (2, 3) \), upper at \( (3, 4) \). So vertical change is \( 4 - 3 = 1 \)? Wait, but let's check the Pythagorean theorem. Wait, maybe I misread. Wait, the two points: one at \( (2, 3) \), one at \( (3, 4) \). So horizontal distance \( a = 3 - 2 = 1 \), vertical distance \( b = 4 - 3 = 1 \)? Wait, but then \( c^2 = 1^2 + 1^2 = 2 \), but maybe the points are different. Wait, no, the grid: the lower blue dot is at \( x = 2 \), \( y = 3 \); the upper blue dot is at \( x = 3 \), \( y = 4 \). So vertical distance \( b \) is \( 4 - 3 = 1 \). Wait, but the options have 1 as a button (the green 1). Wait, maybe that's it.

Answer:

1 (the button labeled "1" in the green square)