Question

determine the following. *

1. which point on a number line is \\(\frac{4}{5}\\) the distance from point \\(-6\\) to 14?

\\(\bigcirc\\) 2
\\(\bigcirc\\) 6
\\(\bigcirc\\) 10
\\(\bigcirc\\) 14
\\(\bigcirc\\) 7
\\(\bigcirc\\) 9
\\(\bigcirc\\) 12
\\(\bigcirc\\) 11
\\(\bigcirc\\) 5
\\(\bigcirc\\) 4
\\(\bigcirc\\) 8

Explanation:

Step1: Calculate distance between -6 and 14

The distance between two points \(a\) and \(b\) on a number line is \(|b - a|\). So, distance between \(-6\) and \(14\) is \(|14 - (-6)| = |20| = 20\).

Step2: Find \(\frac{4}{5}\) of this distance

Calculate \(\frac{4}{5} \times 20\). \(\frac{4}{5} \times 20 = 16\).

Step3: Find the point from -6

Start at \(-6\) and move \(16\) units towards \(14\) (since we want the point \(\frac{4}{5}\) of the distance from \(-6\) to \(14\)). So, \(-6 + 16 = 10\).

Answer:

10 (corresponding to the option "10")