If vertices of a triangle have coordinates (-2, 2), : DS Archive
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# If vertices of a triangle have coordinates (-2, 2),

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Manager
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If vertices of a triangle have coordinates (-2, 2), [#permalink]

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10 Dec 2009, 12:42
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If vertices of a triangle have coordinates $$(-2, 2), (3, 2), (x, y)$$ , what is the area of the triangle?

1. $$|y - 2| = 1$$
2. angle at the vertex $$(x, y)$$ equals 90 degrees
Manager
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Re: If vertices of a triangle have coordinates (-2, 2), (3, 2) [#permalink]

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10 Dec 2009, 20:50
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swatirpr wrote:
If vertices of a triangle have coordinates $$(-2, 2), (3, 2), (x, y)$$ , what is the area of the triangle?

1. $$|y - 2| = 1$$
2. angle at the vertex $$(x, y)$$ equals 90 degrees

It's A.
Stmt1 tells us that y can be 1 or 3. In either case area will be same. Sufficient.

Stmt2 tells us nothing about y, which we need in order to calculate the area of the triangle. Insufficient.
Manager
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Re: Bacteria Population, Area of Triangle [#permalink]

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16 Dec 2009, 06:19
I have doubt for S1: even though Y can take 1 or 3 but we dont know the value of X so how can we calulate the area?

Now for S2: if the angle is 90 then slope of the line (-2,2) and (x,y) * 1/ slope of the line (3,2) and (x,y) = -1

i.e. y-2/x+2 * x-3/y-2 = -1 on solving we get x but dont know y so insuff
Manager
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Re: Bacteria Population, Area of Triangle [#permalink]

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16 Dec 2009, 06:35
sagarsabnis wrote:
I have doubt for S1: even though Y can take 1 or 3 but we dont know the value of X so how can we calulate the area?

Now for S2: if the angle is 90 then slope of the line (-2,2) and (x,y) * 1/ slope of the line (3,2) and (x,y) = -1

i.e. y-2/x+2 * x-3/y-2 = -1 on solving we get x but dont know y so insuff

Plot $$(-2, 2), (3, 2),$$ and $$y=3$$ and $$y=1$$

Consider line passing through (-2, 2) and (3, 2) base. You find that irrespective of value of x the height of triangle with vertex y=3 or y=1 is 1.

Hope its clear now.
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Re: Bacteria Population, Area of Triangle [#permalink]

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16 Dec 2009, 06:41
hi.... area will be same irrespective of value of x...
area will be (5(dist between two given pts..its llel to x axis)*ht)/2...
ht will be basically dist to y axis , which will depend on only y's value and y is 1 in both cases..
ans A
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Re: Bacteria Population, Area of Triangle   [#permalink] 16 Dec 2009, 06:41
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