Question

1. use the figure below for questions 1 - 4. give another name for line r. 2. name the intersection of lines r and s. 3. name three collinear points. 4. give another name for plane n. 5. use the figure below for questions 5 - 8. name a point coplanar to point k. 6. name the intersection of plane r and line jl. 7. name three non - collinear points. 8. give another name for line jk. 9. if de = 4x - 1, ef = 9, and df = 9x - 22, find the value of x.

Explanation:

Step1: Use segment - addition postulate

Since $DF=DE + EF$, we substitute the given expressions: $9x - 22=(4x - 1)+9$.

Step2: Simplify the right - hand side

$(4x - 1)+9=4x+(-1 + 9)=4x + 8$. So the equation becomes $9x - 22=4x + 8$.

Step3: Isolate the variable terms

Subtract $4x$ from both sides: $9x-4x - 22=4x-4x + 8$, which simplifies to $5x-22 = 8$.

Step4: Isolate the variable

Add 22 to both sides: $5x-22 + 22=8 + 22$, getting $5x=30$.

Step5: Solve for x

Divide both sides by 5: $\frac{5x}{5}=\frac{30}{5}$, so $x = 6$.

Answer:

$x = 6$