SOLUTION: find the fourth vertex of three coordinate points (0,10) (30,10) (20,-30)find fourth point. how many other points could be vertex?

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Question 29781: find the fourth vertex of three coordinate points (0,10) (30,10) (20,-30)find fourth point. how many other points could be vertex?
Answer by venugopalramana(3286) (Show Source):
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find the fourth vertex of three coordinate points (0,10) (30,10) (20,-30)find fourth point. how many other points could be vertex?
DONT USE VERTEX FOR ALL POINTS...GENERALLY IN THESE PROBLEMS WE HAVE ONE VERTEX ONLY.
LET THE EQUATION BE
(X-H)^2=A(Y-K)...PUTTING THE 3 POINTS WE GET 3 EQNS...
(0-H)^2=H^2=A(10-K).........I
(30-H)^2=A(10-K)....................II
(20-H)^2=A(-30-K)........................III
EQN.I/EQN.II....
H^2/(30-H)^2=1
H/(30-H)=1
H=30-H
2H=30
H=15
EQN.II/EQN.III.....
(30-15)^2/(20-15)^2=(10-K)/(-30-K)
225/25=9=(K-10)/(K+30)
9K+270=K-10
8K=-260
K=-32.5
SUBSTITUTING IN ...I...
(-15)^2=225=A(10+32.5)=42.5A
A=225/42.5=2250/425=90/17
HENCE THE EQUATION IS
(X-15)^2=(90/17)(Y+32.5)....HENCE VERTEX IS GIVEN BY
X-15=0.....OR....X=15.....AND ......Y=-32.5.