Points on a perpendicular bisector or on an angle bisector

Answer Key - Grade 10 Math Worksheet

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

1. 1.

   Kira draws the perpendicular bisector of kite crossbar DF. Q is on it, QD = 3x + 5 and QF = 5x − 13, in cm. How long is QD?

   32
2. 2.

   Luz folds paper along the perpendicular bisector of edge SU. H is on it, HS = 2x + 15 and HU = 5x − 6, in inches. How long is HS?

   29
3. 3.

   Milo walks the perpendicular bisector of park path CY. Q is on it, QC = 5x − 6 and QY = 2x + 18, in m. How long is QC?

   34
4. 4.

   Noah pegs a rope on the perpendicular bisector of tent edge WD. S is on it, SW = x + 21 and SD = 4x − 9, in ft. How long is SW?

   31
5. 5.

   Pia hangs a lamp in a corner. Q is on ray VS, the bisector of ∠CVW. Its distances to the sides are 3x + 1 and x + 13, in ft. What is x?

   6
6. 6.

   Ren plants a tree where paths meet. Q is on ray GH, the bisector of ∠DGF. Its distances to the sides are 5x − 7 and 2x + 11, in m. What is x?

   6
7. 7.

   Tala marks a well between two roads. S is on ray HV, the bisector of ∠UHY. Its distances to the sides are 4x + 1 and 6x − 13, in km. What is x?

   7
8. 8.

   Ari checks a point Q drawn above a kite's crossbar DF, whose midpoint is G. QD = 9 cm and QF = 9 cm. Is Q on the perpendicular bisector of DF?

   • No: 9 cm is not half of DF.
   • We cannot tell: no right angle is marked at G.
   • No: Q is not on segment DF.
   • Yes: Q is the same distance from D and from F.
9. 9.

   Bo checks where a bench H stands near a straight park path CW, whose midpoint is S. HC = 11 m and HW = 13 m. Is H on the perpendicular bisector of CW?

   • We cannot tell: no right angle is marked at S.
   • No: H is 11 m from C but 13 m from W.
   • Yes: 11 m and 13 m are close enough to count as equal.
   • Yes: in the sketch, H looks as if it is straight above S.
10. 10.

    Esme checks a lamp hook Q inside the shelf corner ∠DVF. QU = QY = 7 inches, with no right angle marked at the sides. Is Q on the bisector of the angle?

    • We cannot tell: QU and QY are not marked at right angles to the sides.
    • Yes: in the sketch, Q looks halfway between the two sides.
    • Yes: Q is 7 inches from both sides.
    • No: 7 inches is too far from the corner V.