Question

pythagorean distance
what is the vertical distance b?
pythagorean formula c² = a² + b²
a=2
b=?

Explanation:

Step1: Identify coordinates of points

The first point (left) is at (2, 1), the second point (right) is at (4, 2).

Step2: Calculate vertical distance

Vertical distance is the difference in y - coordinates. So \( b = 2 - 1 = 1 \)? Wait, no, wait the grid: Wait, the first point is at y = 1, the second at y = 2? Wait no, the dashed line for b: the lower point is at y = 1, upper at y = 2? Wait no, looking at the graph: the blue dot at the bottom (for vertical distance) is at y = 1, and the upper blue dot is at y = 2? Wait no, wait the vertical distance: the y - coordinate of the left point is 1, the y - coordinate of the right point is 2. So vertical distance \( b = 2 - 1 = 1 \)? Wait, but let's check the horizontal distance a = 2 (from x = 2 to x = 4, so 4 - 2 = 2). Wait, maybe I misread. Wait the left point is (2,1), right point is (4,2). So vertical change: 2 - 1 = 1, horizontal change: 4 - 2 = 2. Wait, but let's confirm with the Pythagorean formula. Wait, maybe the vertical distance is the difference in y - values. So if the lower point is at y = 1 and upper at y = 2, then \( b = 2 - 1 = 1 \)? But wait, the options? Wait no, maybe I made a mistake. Wait the left point: x = 2, y = 1; right point: x = 4, y = 2. So vertical distance (b) is |2 - 1| = 1? Wait, but let's check again. Wait the dashed line for b: from y = 1 to y = 2, so that's 1 unit. So \( b = 1 \).

Wait, but let's re - examine. The horizontal distance a is 2 (from x = 2 to x = 4, so 4 - 2 = 2). The vertical distance: the y - coordinate of the left point is 1, the y - coordinate of the right point is 2. So vertical distance \( b = 2 - 1 = 1 \).

Answer:

1