Fractions and Decimals

Discrete Mathematics

Differential Equations

Solved on Jan 12, 2024

Find the length of $Y X$ if $Y$ is between $X$ and $Z$ , $Y Z=4$ , and $X Z=12$ .

STEP 1

Assumptions
1. $Y$ is a point on the line segment $XZ$ .
2. $YZ = 4$ units.
3. $XZ = 12$ units.
4. We need to find the length of $XY$ .

STEP 2

Since $Y$ is between $X$ and $Z$ , the segments $XY$ and $YZ$ are consecutive and add up to the total length of $XZ$ .
$XY + YZ = XZ$

STEP 3

Now, plug in the given values for $YZ$ and $XZ$ to set up the equation.
$XY + 4 = 12$

STEP 4

Subtract 4 from both sides of the equation to solve for $XY$ .
$XY = 12 - 4$

STEP 5

Calculate the length of $XY$ .
$XY = 12 - 4 = 8$
The length of $XY$ is 8 units.

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