Question

pythagorean distance
what is the horizontal distance a?
points: (4, 5) (-5, -7)
a = δx =?
pythagorean formula c² = a² + b²

Explanation:

Step1: Recall the formula for horizontal distance

The horizontal distance (Δx) between two points \((x_1, y_1)\) and \((x_2, y_2)\) is given by \( \Delta x = x_2 - x_1 \) (or \( x_1 - x_2 \), we take the absolute value conceptually, but here we can just compute the difference).
Given points \((4, 5)\) and \((-5, -7)\), let \( x_1 = 4 \) and \( x_2 = -5 \).

Step2: Calculate the difference in x - coordinates

Substitute the values into the formula: \( \Delta x = -5 - 4 \)
\( -5 - 4 = -9 \), but since distance is a magnitude (and here we are looking for the horizontal change, the absolute value of -9 is 9, but let's check the calculation again. Wait, actually, the horizontal distance is the absolute difference, but the Δx here is \( x_2 - x_1=-5 - 4=-9 \), but the magnitude (the value we need for the horizontal leg of the right triangle) is \( | - 9| = 9 \)? Wait, no, wait. Wait, the two points are \((4,5)\) and \((-5,-7)\). The horizontal change is \( x_2 - x_1=-5 - 4=-9 \), but the length of the horizontal side (the distance) is the absolute value, so \( |\Delta x|=| - 9| = 9 \). Wait, but let's check the options. Wait, maybe I made a mistake. Wait, no, the horizontal distance is the difference in x - coordinates. Let's recast: \( \Delta x=x_1 - x_2=4-(-5)=4 + 5 = 9 \). Ah, right! Because if we take the first x as 4 and the second as -5, then \( \Delta x = 4-(-5)=9 \). So the horizontal distance a is 9.

Answer:

9