← Back to Points, Lines & Planes

Points, Lines & Planes - Worksheet 9 - 10th Grade

Hard

Identify lines, rays and segments, use labeled diagrams, and reason about collinearity and planes.

hard: Combine diagram reasoning with line and plane postulates.

30 problems · 10-15 minutes · Skills: geometry, vocabulary, notation

About This Worksheet

This hard-level worksheet contains 30 problems designed for 10th Grade students practicing points, lines & planes. Hard worksheets feature challenging problems including multi-step questions, missing values, and real-world applications to push students further.

Recognize points and read labels from left to right on a diagram.

  • Identify lines, rays and segments, use labeled diagrams, and reason about collinearity and planes.
  • A ray name starts with its endpoint. Two distinct points determine a line; three non-collinear points determine a plane.

How to Solve: Worked Example

Example Problem: A, B and C lie on a line in that order. AB = 4 cm and BC = 7 cm. Find AC.
Solution Steps:
  1. B lies between A and C, so the two segments do not overlap.
  2. Use segment addition: AC = AB + BC.
  3. Add: 4 + 7 = 11 cm.
Answer: 11 cm
Tip: A ray name starts with its endpoint. Two distinct points determine a line; three non-collinear points determine a plane.
1
F, G, H are collinear in that order. FG = 4 cm and GH = 30 cm. Find the distance from F to the midpoint of FH.
FGH
Diagram not to scale.
2
Points A and B are distinct. How many lines pass through both?
3
F, G, H are collinear in that order. FG = 27 cm and GH = 4 cm. Find the distance from F to the midpoint of FH.
FGH
Diagram not to scale.
4
Points C, D, E are non-collinear. How many planes contain all three?
5
K, L, M are collinear in that order. KL = 15 cm and LM = 3 cm. Find the distance from K to the midpoint of KM.
KLM
Diagram not to scale.
6
Points T, U, V are collinear. Do these three points determine exactly one plane?
7
B, C, D are collinear in that order. BC = 20 cm and CD = 23 cm. Find the distance from B to the midpoint of BD.
BCD
Diagram not to scale.
8
Two distinct planes both contain line QR. What is their intersection?
9
B, C, D are collinear in that order. BC = 9 cm and CD = 12 cm. Find the distance from B to the midpoint of BD.
BCD
Diagram not to scale.
10
Points N and P are distinct. How many lines pass through both?
11
R, S, T are collinear in that order. RS = 14 cm and ST = 3 cm. Find the distance from R to the midpoint of RT.
RST
Diagram not to scale.
12
Points W, X, Y are non-collinear. How many planes contain all three?
13
H, J, K are collinear in that order. HJ = 18 cm and JK = 3 cm. Find the distance from H to the midpoint of HK.
HJK
Diagram not to scale.
14
Points X, Y, Z are collinear. Do these three points determine exactly one plane?
15
R, S, T are collinear in that order. RS = 25 cm and ST = 17 cm. Find the distance from R to the midpoint of RT.
RST
Diagram not to scale.
16
Two distinct planes both contain line DE. What is their intersection?
17
Z, A, B are collinear in that order. ZA = 22 cm and AB = 27 cm. Find the distance from Z to the midpoint of ZB.
ZAB
Diagram not to scale.
18
Points X and Y are distinct. How many lines pass through both?
19
E, F, G are collinear in that order. EF = 11 cm and FG = 5 cm. Find the distance from E to the midpoint of EG.
EFG
Diagram not to scale.
20
Points P, Q, R are non-collinear. How many planes contain all three?
21
Z, A, B are collinear in that order. ZA = 27 cm and AB = 6 cm. Find the distance from Z to the midpoint of ZB.
ZAB
Diagram not to scale.
22
Points W, X, Y are collinear. Do these three points determine exactly one plane?
23
V, W, X are collinear in that order. VW = 27 cm and WX = 7 cm. Find the distance from V to the midpoint of VX.
VWX
Diagram not to scale.
24
Two distinct planes both contain line EF. What is their intersection?
25
M, P, R are collinear in that order. MP = 10 cm and PR = 26 cm. Find the distance from M to the midpoint of MR.
MPR
Diagram not to scale.
26
Points A and C are distinct. How many lines pass through both?
27
Z, B, D are collinear in that order. ZB = 12 cm and BD = 23 cm. Find the distance from Z to the midpoint of ZD.
ZBD
Diagram not to scale.
28
Points F, H, K are non-collinear. How many planes contain all three?
29
N, Q, S are collinear in that order. NQ = 4 cm and QS = 2 cm. Find the distance from N to the midpoint of NS.
NQS
Diagram not to scale.
30
Points F, H, K are collinear. Do these three points determine exactly one plane?

Answer Key

1. 17 cm2. 13. 15.5 cm4. 15. 9 cm6. No. Infinitely many planes contain the line.7. 21.5 cm8. line QR9. 10.5 cm10. 111. 8.5 cm12. 113. 10.5 cm14. No. Infinitely many planes contain the line.15. 21 cm16. line DE17. 24.5 cm18. 119. 8 cm20. 121. 16.5 cm22. No. Infinitely many planes contain the line.23. 17 cm24. line EF25. 18 cm26. 127. 17.5 cm28. 129. 3 cm30. No. Infinitely many planes contain the line.

Practice next

Report a question or answer error

Frequently Asked Questions

How do I download this points, lines & planes - worksheet 9 worksheet?

Click "Download PDF" for a file, or "Print" to use your browser. You can save it as a PDF or print it directly. The answer key will be on a separate page.

How do I find worksheets at different difficulty levels?

Each subtopic has 10 worksheets: Worksheets 1-3 are Easy, 4-7 are Medium, and 8-10 are Hard. Start with Easy worksheets to build confidence, then progress to harder ones.

What skills does this basics of geometry worksheet cover?

This worksheet focuses on geometry, vocabulary, notation. It is designed for 10th Grade students and provides structured practice through varied problem types with a worked example to guide students before they begin.

Can I use this worksheet in my classroom?

Yes. All worksheets on K12Worksheets are free for classroom use. You can print copies for your entire class. With 10 worksheets per subtopic at three difficulty levels, you have plenty of options for differentiated instruction and individualized practice.

How many problems are on this worksheet?

This worksheet contains 30 problems. It typically takes 10-15 minutes to complete. An answer key with all solutions is included so parents and teachers can check work quickly.