Question

question 4(multiple choice worth 1 points) (04 03 mc) what point on the number line is \\(\frac{2}{5}\\) of the way from the point -9 to the point 17? \\(\circ -3.8\\) \\(\circ 1.4\\) \\(\circ 3.2\\) \\(\circ 6.6\\)

Explanation:

Step1: Find the distance between -9 and 17

The distance between two points \(a\) and \(b\) on the number line is \(|b - a|\). So, the distance between -9 and 17 is \(|17 - (-9)| = |17 + 9| = 26\).

Step2: Calculate \(\frac{2}{5}\) of the distance

We need to find \(\frac{2}{5}\) of 26. So, \(\frac{2}{5} \times 26 = \frac{52}{5} = 10.4\)? Wait, no, wait. Wait, the formula for a point that is \(\frac{m}{n}\) of the way from \(a\) to \(b\) is \(a + \frac{m}{n}(b - a)\). Let's use that. Here, \(a = -9\), \(b = 17\), and \(\frac{m}{n} = \frac{2}{5}\). So, first, find \(b - a = 17 - (-9) = 26\). Then, \(\frac{2}{5}\) of 26 is \(\frac{2}{5} \times 26 = \frac{52}{5} = 10.4\)? Wait, no, wait, the formula is \(a + \frac{m}{n}(b - a)\). So, substituting the values: \(-9 + \frac{2}{5}(17 - (-9)) = -9 + \frac{2}{5}(26) = -9 + \frac{52}{5}\). Convert -9 to fifths: \(-9 = -\frac{45}{5}\). So, \(-\frac{45}{5} + \frac{52}{5} = \frac{7}{5} = 1.4\)? Wait, that's 1.4. Wait, but the options are -3.8, 1.4, 3.2, 6.6. Wait, maybe I made a mistake. Wait, let's recalculate. \(b - a = 17 - (-9) = 26\). \(\frac{2}{5}\) of 26 is \(\frac{52}{5} = 10.4\). Then, add that to \(a\) (which is -9): \(-9 + 10.4 = 1.4\). Yes, that's 1.4. So the point is 1.4.

Answer:

1.4 (corresponding to the option with 1.4)