Question

pythagorean distance
what is the horizontal distance a?
(there is a coordinate grid with two blue dots on the x - axis at x = - 3 and x = 4, and a right triangle with legs a, b and hypotenuse c. the formula c² = a² + b² is shown at the bottom. on the right, there are number buttons and square root buttons with approximate values.)

Explanation:

Step1: Identify coordinates of points

The left blue point is at \( x = -3 \), \( y = 1 \). The right blue point is at \( x = 4 \), \( y = 1 \). Since it's horizontal distance, \( y \)-coordinates are same, so vertical distance \( b = 0 \) (or we can see the vertical change is 0). But actually, for horizontal distance between two points \((x_1,y_1)\) and \((x_2,y_2)\) with \( y_1 = y_2 \), the distance is \( |x_2 - x_1| \).

Step2: Calculate horizontal distance

Using \( x_1 = -3 \), \( x_2 = 4 \), the horizontal distance \( a = |4 - (-3)| = |4 + 3| = 7 \)? Wait, no, wait the graph: Wait, the left point is at \( x=-3 \), right at \( x = 4 \). Wait, but maybe the horizontal segment: Wait, the left blue dot is at \( x=-3 \), \( y = 1 \) (since it's on \( y = 1 \) line). The right blue dot is at \( x = 4 \), \( y = 1 \). So the horizontal distance is \( 4 - (-3) = 7 \)? Wait, but let's check the grid. Wait, from \( x=-3 \) to \( x = 4 \), the number of units: from -3 to 0 is 3, 0 to 4 is 4, total 3 + 4 = 7. Wait, but maybe I misread. Wait, the horizontal line is at \( y = 1 \)? Wait, no, the line is at \( y = 1 \)? Wait, the graph has \( y \)-axis with 0,1,2,... and \( x \)-axis. Wait, the blue dots are on \( y = 1 \) (since the horizontal line is \( y = 1 \)). So the horizontal distance between \( x=-3 \) and \( x = 4 \) is \( 4 - (-3) = 7 \). So \( a = 7 \).

Answer:

7