Question

1. use structure suppose a, b, and c are all negative numbers. how do you find the distance between points (a, b) and (a, c)?

Explanation:

Step1: Recall the distance formula for vertical points

For two points \((x_1,y_1)\) and \((x_2,y_2)\), if \(x_1 = x_2\), the distance \(d=\vert y_1 - y_2\vert\). Here \(x_1=a,x_2 = a,y_1 = b,y_2=c\).

Step2: Apply the formula

Substitute \(y_1 = b\) and \(y_2=c\) into the formula. The distance \(d=\vert b - c\vert\). Since \(b\) and \(c\) are negative numbers, \(\vert b - c\vert=\vert c - b\vert\). For example, if \(b=-2\) and \(c = -5\), \(\vert-2-(-5)\vert=\vert-2 + 5\vert=\vert3\vert = 3\) and \(\vert-5-(-2)\vert=\vert-5 + 2\vert=\vert-3\vert=3\)

Answer:

The distance between the points \((a,b)\) and \((a,c)\) is \(\vert b - c\vert\) (or \(\vert c - b\vert\))