Question

pythagorean distance
what is the vertical distance b?
points: (4, 5) (-5, -7)
a = δx = 9
b = ?
pythagorean formula c² = a² + b²
0 1 2
3 4 5
6 7 8
9 10 12
13 14 15
√2 ≈1.4 √5 ≈2.2 √17 ≈4.1
√34 ≈5.8 √45 ≈6.7 √98 ≈9.9
√104 ≈10.2 √148 ≈12.2 √250 ≈15.8

Explanation:

Step1: Recall vertical distance formula

Vertical distance (Δy) between two points \((x_1,y_1)\) and \((x_2,y_2)\) is \(|y_1 - y_2|\).

Step2: Substitute values

Given points \((4, 5)\) and \((-5, -7)\), \(y_1 = 5\), \(y_2=-7\). So \(b=\Delta y=|5 - (-7)|=|5 + 7| = 12\)? Wait, no, wait. Wait, wait, let's recalculate. Wait, \(y_1 = 5\), \(y_2=-7\), so \(5-(-7)=5 + 7 = 12\)? But wait, the options have 12? Wait, no, wait, maybe I made a mistake. Wait, no, the vertical distance is the difference in y - coordinates. So \(|y_1 - y_2|=|5 - (-7)|=12\)? But wait, the options have 12? Wait, but let's check again. Wait, the points are \((4,5)\) and \((-5,-7)\). So the y - coordinates are 5 and -7. The difference is \(5-(-7)=12\). So \(b = 12\)? Wait, but let's check the options. The options have 12 in the fourth row, third column. Wait, but maybe I messed up. Wait, no, vertical distance is the absolute difference of the y - values. So \(|5 - (-7)|=12\). So \(b = 12\).

Wait, but wait, the horizontal distance \(a=\Delta x=|4-(-5)|=|4 + 5| = 9\), which matches the given \(a = 9\). Then vertical distance is \(|5-(-7)|=12\). So \(b = 12\).

Answer:

12