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Co-ordinate Geometry

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Co-ordinate Geometry

by PGMAT » Sat Aug 11, 2012 5:17 am
if vertices of triangle have coordinates (1,1), (4,1), and (x,y) , what is the area of the triangle?
1. y^2-2y-3=0
2.x^2 = y^2

[spoiler]OA is A. Can some one explain how A alone is sufficient. OE says its possible to calcualte area since height is 2. But my question is, even though y=3 or y=-1, it depends on the value of x to determine if (x,y) is right angle? Please explain[/spoiler]
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Source: — Data Sufficiency |
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by niketdoshi123 » Sat Aug 11, 2012 6:29 am
PGMAT wrote:if vertices of triangle have coordinates (1,1), (4,1), and (x,y) , what is the area of the triangle?
1. y^2-2y-3=0
2.x^2 = y^2
Area of a triangle = 1/2 * base * height
From the figure we know the base of the triangle = 4 - 1 = 3
and the height of the triangle = |y - 1|
Area of the triangle = 1/2 * 3 * |(y-1)|
So if we know the value of y , we can find the area of the triangle

Note: Value of x is not important to find height of the triangle.
Statement1:
y² - 2y - 3 = 0
=> (y-3)(y+1) = 0
=> y = 3 or y = -1
for y = 3
|y-1| = |2| = 2
and for y = -1
|y-1| = |-2| = 2

Since we are getting a unique value of |y-1|
This statement is sufficient to answer

statement 2:
x² = y²
We can get infinite values of y satisfying this equation.
Hence insufficient

The correct answer is A
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