Question

in the figure below, x lies between w and y. find the location of x so that the ratio of wx to xy is 1 to 2. w -16, x ?, y 5. location of x : box

Explanation:

Step1: Find the distance between W and Y

The coordinate of W is -16 and the coordinate of Y is 5. The distance \( d \) between two points \( a \) and \( b \) on a number line is \( |b - a| \). So, \( d = |5 - (-16)| = |5 + 16| = 21 \).

Step2: Determine the length of WX and XY

Given the ratio of \( WX \) to \( XY \) is \( 1:2 \). Let \( WX = x \) and \( XY = 2x \). Then \( WX + XY = WY \), so \( x + 2x = 21 \), which simplifies to \( 3x = 21 \). Solving for \( x \), we get \( x=\frac{21}{3}=7 \). So, \( WX = 7 \).

Step3: Find the coordinate of X

To find the coordinate of X, we start from the coordinate of W (-16) and move \( WX = 7 \) units towards Y (since X is between W and Y). So, the coordinate of X is \( -16 + 7=-9 \).

Answer:

-9