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Source: Beat The GMAT — Problem Solving |
-
neelgandham
- Community Manager
- Posts: 1060
- Location: Utrecht, The Netherlands
- Thanked: 318 times
Lala,
I think your solution is incomplete. Do correct me if I am wrong!
Q: Three points (0,3), (-2,0), and (b,0) composed a right triangle. b=?
Solution :
Let point (0,3) be labelled A
Let point (-2,0) be labelled B
Let point (b,0) be labelled C
Case 1: If line segments AC(on Y axis), BC(on X axis) are perpendicular(Red triangle in the attachment) and line segment AB is the hypotenuse, then line segments AC and BC meet at the origin (0,0). The value of b is 0
Case 2: If line segments AB(on X axis), BC(On X axis) are perpendicular and line segment AC is the hypotenuse. This is impossible as points B and C are on the same line(X axis) and angle between line segments AB and BC is a constant = Inverse Tan(3/2) !=90 degress
Case 3: If line segments AB,AC are perpendicular (Yellow triangle in the attachment) and line segment AB is the hypotenuse, then the product of slopes of AB and AC should be equal to -1.i.e. Slope of AB * Slope of AC = -1
(3/2)*(3/-b)=-1
b = 4.5
So the value of b can be 0 or 4.5
I think your solution is incomplete. Do correct me if I am wrong!
Q: Three points (0,3), (-2,0), and (b,0) composed a right triangle. b=?
Solution :
Let point (0,3) be labelled A
Let point (-2,0) be labelled B
Let point (b,0) be labelled C
Case 1: If line segments AC(on Y axis), BC(on X axis) are perpendicular(Red triangle in the attachment) and line segment AB is the hypotenuse, then line segments AC and BC meet at the origin (0,0). The value of b is 0
Case 2: If line segments AB(on X axis), BC(On X axis) are perpendicular and line segment AC is the hypotenuse. This is impossible as points B and C are on the same line(X axis) and angle between line segments AB and BC is a constant = Inverse Tan(3/2) !=90 degress
Case 3: If line segments AB,AC are perpendicular (Yellow triangle in the attachment) and line segment AB is the hypotenuse, then the product of slopes of AB and AC should be equal to -1.i.e. Slope of AB * Slope of AC = -1
(3/2)*(3/-b)=-1
b = 4.5
So the value of b can be 0 or 4.5
- Attachments
-
Anil Gandham
Welcome to BEATtheGMAT | Photography | Getting Started | BTG Community rules | MBA Watch
Check out GMAT Prep Now's online course at https://www.gmatprepnow.com/
Welcome to BEATtheGMAT | Photography | Getting Started | BTG Community rules | MBA Watch
Check out GMAT Prep Now's online course at https://www.gmatprepnow.com/
-
ronnie1985
- Legendary Member
- Posts: 626
- Location: Ahmedabad
- Thanked: 31 times
By pythagoras theorem
(b+2)^2 = (2^2+3^2)+(b^2+3^2)
b = 4.5
(b+2)^2 = (2^2+3^2)+(b^2+3^2)
b = 4.5
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