Points on a perpendicular bisector or on an angle bisector

Answer Key - Grade 10 Math Worksheet - Challenge Me

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

1. 1.

   Kira hangs a lamp Q in a room corner. Q is 6 ft from each side of ∠CVW. m∠CVQ = (3x + 4)° and m∠QVW = (5x − 12)°. What is m∠CVW?

   56
2. 2.

   Milo marks a lookout Q between two roads. Q is 4 km from each side of ∠UHY. m∠UHQ = (6x − 5)° and m∠QHY = (4x + 9)°. What is m∠UHY?

   74
3. 3.

   Noah sets a cup D in a rug corner. D is 7 inches from each side of ∠SWC. m∠SWD = (x + 24)° and m∠DWC = (3x − 10)°. What is m∠SWC?

   82
4. 4.

   Pia measures a kite. Q is on the perpendicular bisector of DF. QD = 3x + 1, QF = 5x − 11 and DG = 2x + 3, in cm. How long is DF?

   30
5. 5.

   Ren folds a paper sheet. H is on the perpendicular bisector of CW. HC = 4x − 2, HW = 2x + 12 and CS = x + 3, in inches. How long is CW?

   20
6. 6.

   Tala maps a park fountain. Q is on the perpendicular bisector of UY. QU = 6x + 5, QY = 3x + 26 and UV = 4x + 2, in m. How long is UY?

   60
7. 7.

   Zee sets up a tent. C is on the perpendicular bisector of SD. CS = 2x + 13, CD = 5x − 11 and SW = 3x − 3, in ft. How long is SD?

   42
8. 8.

   Ari plots two towns D and F on a map grid and checks a spot Q: D(0, 2), F(6, 4) and Q(3, 7). Is Q on the perpendicular bisector of DF?

   • No: QD² = 34 but QF² = 18, so QD ≠ QF.
   • Yes: Q is higher than both D and F.
   • Yes: Q is 3 squares across from D and 3 squares across from F.
   • Yes: Q is straight above the midpoint (3, 3) of DF.
9. 9.

   Esme plots two classroom doors C and U on a grid and checks a spot H for a sign: C(3, 1), U(7, 3) and H(4, 6). Is H on the perpendicular bisector of CU?

   • No: HC² = 26 but HU² = 18, so HC ≠ HU.
   • Yes: H is 3 squares above U and 3 squares across from U.
   • Yes: H is higher than both C and U.
   • Yes: HC and HU are both 6 squares.
10. 10.

    Jun plots two trees Y and V on a grid and checks a spot D for a lamp: Y(2, 3), V(6, 1) and D(6, 6). Is D on the perpendicular bisector of YV?

    • Yes: DY² = 25 and DV² = 25, so DY = DV = 5.
    • No: D is not on segment YV.
    • No: D is not straight above the midpoint (4, 2) of YV.
    • No: DY is 7 squares and DV is 5 squares.