Question

in the figure below, y lies between x and z. find the location of y so that the ratio of xy to yz is 2 to 1. image of number line with x at -16, y at ?, z at 5 location of y : box buttons

Explanation:

Step1: Find the length of XZ

The coordinates of X is -16 and Z is 5. The distance between X and Z is $5 - (-16) = 21$.

Step2: Determine the length of XY and YZ

Since the ratio of XY to YZ is 2:1, let XY = 2x and YZ = x. Then $2x + x = 21$, so $3x = 21$ and $x = 7$. Thus, XY = 14 and YZ = 7.

Step3: Find the coordinate of Y

Starting from X (-16), moving 14 units towards Z (since XY = 14), the coordinate of Y is $-16 + 14 = -2$.

Answer:

-2