Question

in the figure below, x lies between w and y. find the location of x so that wx is \\(\frac{2}{5}\\) of wy. number line with w at -8, x at ?, y at 17 location of x : \\(\square\\) buttons: 5, x

Explanation:

Step1: Calculate the length of \( WY \)

The coordinates of \( W \) is \(-8\) and the coordinates of \( Y \) is \( 17 \). The distance between two points on a number line is the absolute difference of their coordinates. So, \( WY = |17 - (-8)| = |17 + 8| = 25 \).

Step2: Find the length of \( WX \)

We know that \( WX=\frac{2}{5}\) of \( WY \). So, \( WX=\frac{2}{5}\times25 = 10 \).

Step3: Determine the location of \( X \)

Since \( W \) is at \(-8\) and we move \( 10 \) units towards \( Y \) (because \( X \) is between \( W \) and \( Y \)) to get to \( X \), we add \( 10 \) to the coordinate of \( W \). So, the coordinate of \( X \) is \(-8 + 10 = 2\).

Answer:

\( 2 \)