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 4 to 3. x is at -21, z is at 7, y is at ?

Explanation:

Step1: Calculate the length of XZ

The coordinates of X is -21 and Z is 7. The distance between X and Z is \( 7 - (-21) = 28 \).

Step2: Determine the lengths of XY and YZ based on the ratio

The ratio of XY to YZ is 4:3, so the total number of parts is \( 4 + 3 = 7 \) parts. Each part has a length of \( \frac{28}{7} = 4 \).

Step3: Calculate the coordinate of Y

The length of XY is \( 4\times4 = 16 \). Starting from X (-21), moving 16 units towards Z, the coordinate of Y is \( -21 + 16 = -5 \).

Answer:

-5