Question

name:____ date:__ per:____ geometry unit 1: geometry basics quiz 1 - 1: points, lines, planes, distance & midpoint use the figure below for questions 1 - 4. 1. give another name for the r. 2. name the intersection of lines r and s. 3. name three collinear points. 4. give another name for plane k. use the figure below for questions 5 - 8. 5. 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. use the figure below for questions 9 - 11. 9. if de = 4x - 1, ef = 9, and df = 9x - 22, find the value of x. 10. if df = 78, de = 5x - 9, and ef = 2x + 10, find ef. 11. if de = 4x + 10, ef = 2x - 1, and df = 9x - 15, find df. © gino wilson (all things algebra, llc), 2014 - 2017

Explanation:

Step1: Recall line - segment addition postulate

For collinear points \(D\), \(E\), and \(F\), \(DE + EF=DF\).

Step2: Solve question 9

Given \(DE = 4x - 1\), \(EF = 9\), and \(DF=9x - 22\). Substitute into \(DE + EF = DF\):
\((4x - 1)+9=9x - 22\)
\(4x+8 = 9x - 22\)
\(8 + 22=9x - 4x\)
\(30 = 5x\)
\(x = 6\)

Step3: Solve question 10

Given \(DF = 78\), \(DE = 5x - 9\), and \(EF = 2x + 10\). Substitute into \(DE + EF = DF\):
\((5x - 9)+(2x + 10)=78\)
\(5x-9 + 2x+10 = 78\)
\(7x+1 = 78\)
\(7x=78 - 1\)
\(7x = 77\)
\(x = 11\)
Then \(EF=2x + 10=2\times11 + 10=22 + 10 = 32\)

Step4: Solve question 11

Given \(DE = 4x + 10\), \(EF = 2x - 1\), and \(DF = 9x - 15\). Substitute into \(DE + EF = DF\):
\((4x + 10)+(2x - 1)=9x - 15\)
\(4x+10 + 2x-1 = 9x - 15\)
\(6x + 9=9x - 15\)
\(9 + 15=9x - 6x\)
\(24 = 3x\)
\(x = 8\)
Then \(DF=9x - 15=9\times8 - 15=72 - 15 = 57\)

Answer:

1. \(x = 6\)
2. \(EF = 32\)
3. \(DF = 57\)