Question

Create a point f anywhere on the screen except for on . draw segments and and find their lengths. what do you notice about the lengths of and . drag point f around on the screen. where must point f lie so that ?

Answer 1

To make AxF = BF, point F must lie on the perpendicular bisector of segment AB.

Step-by-step explanation:

In order to make AxF = BF, point F must lie on the perpendicular bisector of segment AB. The perpendicular bisector is a line that passes through the midpoint of AB and is perpendicular to AB. Any point on this line will have the same distance from A and B, resulting in AxF = BF.

For example, if A is at (2, 3) and B is at (8, 3), the midpoint of AB is (5, 3) and the line perpendicular to AB passing through (5, 3) can be any line with an equation of the form x = 5. Any point on this line will satisfy AxF = BF.

So, in conclusion, for AxF = BF, point F must lie on the perpendicular bisector of segment AB.