Geometry: An Interactive Journey to Mastery

Lesson 12: Equidistance—A Focus on Distance

1. Which of the following points are equidistant from A ͼ௘௘ͽDQGB ͼ௘௘ͽ"
   D௘ͽ P (3, 6)
   E௘ͽ Q (2,7)
   F௘ͽ R (6, 3)
   G௘ͽ S (12, 9 )
   H௘ͽ T (2,3)
   I௘ͽ U (10, 4 )
   ͼ௘:KDWLVDQHI¿FLHQWZD\WRKDQGOHWKLVTXHVWLRQ"௘ͽ


2. D௘ͽ :LWKRXWSORWWLQJWKHSRLQWVVKRZWKDWA ͼ௘௘ͽB ͼ௘í௘ͽDQGC ͼ௘í௘ͽIRUPDQ
   isosceles triangle.
   E௘ͽ &RPSXWHWKHPLGSRLQWVRILWVWKUHHVLGHV
   F௘ͽ 6KRZWKDWWKHPLGSRLQWVDOVRIRUPDQLVRVFHOHVWULDQJOH


3. Given: P is on the perpendicular bisector of AB.
   P is on the perpendicular bisector of BC.
   Prove: PA = PC.
   ͼ௘6HHFigure 12.4௘ͽ

Problems

A

B

P C

Figure 12.4