Question

15, find the distance between each pair of points.

1. (-6.1, -8.4) and (-6.1, -4.2) 12. (12
2. (-5.4, 4.7) and (0.6, 4.7) 15.

Explanation:

Step1: Identify the formula for distance

Since the \(x -\)coordinates are the same (\(x_1=x_2 = - 6.1\)), the distance formula simplifies to \(d=\vert y_2 - y_1\vert\). Here, \(y_1=-8.4\) and \(y_2=-4.2\).

Step2: Calculate the absolute - value expression

\(\vert-4.2\vert-\vert-8.4\vert\) (using the property that for two numbers \(a\) and \(b\) with the same \(x -\)coordinate, \(d=\vert y_2\vert-\vert y_1\vert\) when \(y_2>y_1\) and \(y_1,y_2<0\)).
\(=4.2-8.4\) (since \(\vert-4.2\vert = 4.2\) and \(\vert-8.4\vert = 8.4\)).
\(=\vert-4.2-(-8.4)\vert=\vert-4.2 + 8.4\vert=\vert4.2\vert = 4.2\) (using the formula \(d=\vert y_2 - y_1\vert\)).

Answer:

\(4.2\)