Question

pythagorean distance
what is the horizontal distance a?
pythagorean formula \\( c^2 = a^2 + b^2 \\)

Explanation:

Step1: Identify coordinates of points

The left point is at \( (2, 3) \), the right point is at \( (3, 4) \). Horizontal distance \( a \) is the difference in x - coordinates.
\( a=\vert3 - 2\vert= 1 \)? Wait, no, wait. Wait, the vertical distance \( b \): difference in y - coordinates is \( 4 - 3 = 1 \)? Wait, no, looking at the grid, the horizontal distance between \( x = 2 \) and \( x = 3 \) is \( 3 - 2=1 \)? Wait, but maybe we use Pythagorean? Wait, no, the horizontal distance \( a \): the x - coordinates of the two points are 2 and 3, so \( a=3 - 2 = 1 \)? Wait, no, maybe I misread. Wait, the two points: let's check the x - values. The first point (left) is at x = 2, the second (right) is at x = 3. So horizontal distance \( a=3 - 2 = 1 \)? But that seems too small. Wait, no, maybe the vertical distance \( b \): y - coordinates are 3 and 4, so \( b = 4 - 3=1 \). Wait, but maybe the length of \( c \) is calculated, but the question is about horizontal distance \( a \), which is the difference in x - coordinates. So \( a=3 - 2 = 1 \)? But the options don't have 1? Wait, no, wait, maybe I made a mistake. Wait, the left point is at (2, 3), the right point is at (3, 4). So horizontal change (a) is \( 3 - 2 = 1 \), vertical change (b) is \( 4 - 3 = 1 \). Wait, but maybe the problem is that the horizontal distance is 1? But the options on the right: wait, the numbers 0 - 15, and then square roots. Wait, maybe I misread the points. Wait, the left point: x = 2, y = 3; right point: x = 3, y = 4. So horizontal distance \( a=3 - 2 = 1 \), vertical distance \( b = 4 - 3=1 \). Then using Pythagorean theorem, \( c^{2}=a^{2}+b^{2}=1 + 1 = 2 \), \( c=\sqrt{2}\approx1.4 \), but the question is about \( a \). Wait, the horizontal distance \( a \) is the difference in x - coordinates, so \( a = 3 - 2=1 \). But the options on the right: the first row of numbers has 0,1,2,3,4,5,6,7,8,9,10,12,13,14,15. Wait, 1 is an option (the second cell in the first row: 1). Wait, maybe that's it.

Wait, no, wait, maybe I messed up. Let's re - check. The horizontal distance between the two points: the x - coordinate of the left point is 2, the x - coordinate of the right point is 3. So \( a=3 - 2 = 1 \). So the horizontal distance \( a \) is 1.

Step2: Confirm with grid

On the coordinate grid, each square is 1 unit. The horizontal movement from x = 2 to x = 3 is 1 unit. So \( a = 1 \).

Answer:

1 (Looking at the options, the number 1 is in the second cell of the first row of the number pad on the right, i.e., the button labeled "1")