Perpendicular and Angle Bisectors in Geometry

Question 1

Given a point X that lies on the perpendicular bisector of segment AB, which relationship must hold between distances XA and XB?

Accepted Answer

XA = XB

Question 2

If a point D satisfies DA = DB, what can be concluded about D's position relative to segment AB?

Accepted Answer

D lies on the perpendicular bisector of AB

Question 3

A point Y lies on the bisector of angle ∠BAC. Which of the following statements is always true?

Accepted Answer

Y is equidistant from sides AB and AC

Question 4

Point Z is inside angle ∠XYZ and satisfies the condition that its distances to the sides XY and XZ are equal. What does this imply about Z?

Accepted Answer

Z lies on the bisector of ∠YXZ

Question 5

What is the equation of the perpendicular bisector of segment PQ with endpoints P(−2, 3) and Q(4, 1)?

Accepted Answer

y = -3/2 x + 9

Given a point X that lies on the perpendicular bisector of segment AB, which relationship must hold between distances XA and XB?