Points, lines, planes and segments: names, notation and lengths

Answer Key - Grade 10 Math Worksheet

Circle the best answer, or write your answer on the line.

1. 1.

   Noah folds a paper strip at point F. DF = (x + 2) cm, FG = (2x + 1) cm and DG = 24 cm. What is x?

   7
2. 2.

   Pia marks a ladder rail at point Q. HQ = (3x + 2) cm, QS = (2x + 3) cm and HS = 50 cm. What is x?

   9
3. 3.

   Ren rides a straight bike path with a rest stop at V. UV = (2x + 5) m, VW = (4x + 1) m and UW = 54 m. What is x?

   8
4. 4.

   Zee ties a bow at point G on a kite string. FG = (2x + 4) cm, GQ = (3x + 1) cm and FQ = 50 cm. How long is GQ, in cm?

   28
5. 5.

   Ari builds a straight toy-train track with a tunnel at U. SU = (4x + 2) m, UW = (x + 9) m and SW = 46 m. How long is UW, in m?

   16
6. 6.

   Esme bikes a straight path with a bench at H. GH = (x + 8) m, HS = (3x + 2) m and GS = 70 m. How long is HS, in m?

   47
7. 7.

   Jun marks two points, D and F, on paper. How many different lines pass through both D and F?

   • infinitely many
   • none
   • exactly one
   • exactly two
8. 8.

   Kira sets three cups on a table, at points G, H and Q, not in a row. How many different planes contain G, H and Q?

   • none
   • infinitely many
   • exactly one
   • exactly three
9. 9.

   Luz marks points S, U and V in a row along the edge of a door. S, U and V lie on one line. How many different planes contain all three?

   • exactly three
   • none
   • infinitely many
   • exactly one
10. 10.

    Noah looks at the two slanted sides of a tent. Each side is part of a plane. What do the two planes share at the top edge?

    • nothing
    • a plane
    • a line
    • a point