Question

pythagorean distance
what is the horizontal distance a?
pythagorean formula c² = a² + b²

Explanation:

Step1: Identify Coordinates

First, find the coordinates of the two points. The top point is at \((-3, 4)\) and the bottom point is at \((4, -3)\).

Step2: Calculate Horizontal Distance

Horizontal distance \(a\) is the difference in \(x\)-coordinates. So, \(a = 4 - (-3)\)? Wait, no, wait. Wait, the horizontal distance between the two points (the bottom point's \(x\) is 4, and the vertical line for the left point is at \(x = -3\)? Wait, no, looking at the graph, the left blue dot (bottom) is at \(x = -3\), \(y = -3\)? Wait, no, the bottom blue dot: let's check the grid. The bottom blue dot is at \(x = -3\), \(y = -3\)? Wait, no, the right blue dot is at \(x = 4\), \(y = -3\). The left blue dot (top) is at \(x = -3\), \(y = 4\). Wait, the horizontal distance \(a\) is between \(x = -3\) and \(x = 4\)? Wait, no, the dashed line for \(a\) is from \(x = -3\) (the vertical line of the bottom left dot) to \(x = 4\) (the bottom right dot). So the horizontal distance \(a\) is \(4 - (-3) = 7\)? Wait, no, wait the grid: each square is 1 unit. Let's count the horizontal squares between \(x = -3\) and \(x = 4\). From -3 to 4: the number of units is \(4 - (-3) = 7\)? Wait, but let's check the vertical distance \(b\). The vertical distance \(b\) is from \(y = -3\) to \(y = 4\), so \(b = 4 - (-3) = 7\)? Wait, no, the vertical distance is \(4 - (-3) = 7\)? Wait, the Pythagorean theorem: \(c^2 = a^2 + b^2\). Wait, maybe I made a mistake. Wait, the top point is \((-3, 4)\), bottom point is \((4, -3)\). So the horizontal change (a) is \(4 - (-3) = 7\), vertical change (b) is \(-3 - 4 = -7\), but distance is absolute, so \(b = 7\). Wait, but let's check the graph again. Wait, the left blue dot (bottom) is at \((-3, -3)\), right blue dot at \((4, -3)\). Top blue dot at \((-3, 4)\). So the horizontal distance \(a\) is between \(x = -3\) and \(x = 4\), so \(a = 4 - (-3) = 7\). Let's verify with the Pythagorean theorem. The length of \(c\) (the hypotenuse) can be calculated, but we need \(a\) (horizontal distance). So the horizontal distance is the difference in \(x\)-coordinates: \(4 - (-3) = 7\).

Answer:

7