GMAT Prep point converison
This topic has expert replies
-
- Senior | Next Rank: 100 Posts
- Posts: 77
- Joined: Tue Mar 10, 2009 3:10 am
- papgust
- Community Manager
- Posts: 1537
- Joined: Mon Aug 10, 2009 6:10 pm
- Thanked: 653 times
- Followed by:252 members
Draw a vertical perpendicular from points P and Q to x-axis and name those points as R and S.
Angle PRO = 90 degrees
Length OR = root(3)
Length PR = 1
Now, we can say that triangle PRO is a 30-60-90 triangle keeping in mind 1:root(3):2 ratio for this type of triangle.
Angle OPR = 60 degrees and Angle POR = 30 degrees
Therefore, Length OP = 2
Now, we know that Angle POQ = 90 degrees [From the diagram]. We also know that Angle POR = 30 degrees.
Therefore, Angle QOS = 180 - (90+30) = 60 degrees
We already have a perpendicular from Point Q to x-axis. So, Angle QSO = 90 degrees.
Therefore, Angle OQS = 180 - (90+60) = 30 degrees
So we have found that Angle OQS = 30, Angle QOS = 60 and Angle QSO = 90
Therefore, Length OS = 1 [Since Angle OQS = 30 degrees]
Length QS = root(3) [Since Angle QOS = 60 degrees]
Length OQ = 2 [Since Angle QSO = 90 degrees]
So, Point (s,t) is [1,root(3)]. Therefore, s is 1.
Let me know if you have any doubts
Angle PRO = 90 degrees
Length OR = root(3)
Length PR = 1
Now, we can say that triangle PRO is a 30-60-90 triangle keeping in mind 1:root(3):2 ratio for this type of triangle.
Angle OPR = 60 degrees and Angle POR = 30 degrees
Therefore, Length OP = 2
Now, we know that Angle POQ = 90 degrees [From the diagram]. We also know that Angle POR = 30 degrees.
Therefore, Angle QOS = 180 - (90+30) = 60 degrees
We already have a perpendicular from Point Q to x-axis. So, Angle QSO = 90 degrees.
Therefore, Angle OQS = 180 - (90+60) = 30 degrees
So we have found that Angle OQS = 30, Angle QOS = 60 and Angle QSO = 90
Therefore, Length OS = 1 [Since Angle OQS = 30 degrees]
Length QS = root(3) [Since Angle QOS = 60 degrees]
Length OQ = 2 [Since Angle QSO = 90 degrees]
So, Point (s,t) is [1,root(3)]. Therefore, s is 1.
Let me know if you have any doubts