Points on a perpendicular bisector or on an angle bisector
Grade 10 Math Worksheet - Challenge Me
Circle the best answer, or write your answer on the line.
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?
Luz plants a tree S where two paths meet. S is 9 m from each side of ∠DGF. m∠DGS = (2x + 11)° and m∠SGF = (4x − 9)°. What is m∠DGF?
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?
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?
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?
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?
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?
Bo plots two park gates G and W on a grid and checks a spot S for a bench: G(2, 1), W(0, 5) and S(5, 5). Is S on the perpendicular bisector of GW?
- Yes: SG² = 25 and SW² = 25, so SG = SW = 5.
- No: S is not straight above the midpoint (1, 3) of GW.
- No: SG is 7 squares and SW is 5 squares.
- No: S is not on segment GW.
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: HC and HU are both 6 squares.
- Yes: H is 3 squares above U and 3 squares across from U.
- Yes: H is higher than both C and U.
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?
- No: DY is 7 squares and DV is 5 squares.
- 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.