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

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Manager
Joined: 13 Oct 2009
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Location: USA
Schools: IU KSB
If vertices of a triangle have coordinates (-2, 2), [#permalink]

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10 Dec 2009, 13:42
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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

Kudos [?]: 101 [0], given: 66

Manager
Joined: 07 Jul 2009
Posts: 222

Kudos [?]: 138 [1], given: 13

Re: If vertices of a triangle have coordinates (-2, 2), (3, 2) [#permalink]

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10 Dec 2009, 21:50
1
KUDOS
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.

Kudos [?]: 138 [1], given: 13

Manager
Joined: 22 Jul 2009
Posts: 194

Kudos [?]: 540 [0], given: 6

Location: Manchester UK
Re: Bacteria Population, Area of Triangle [#permalink]

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16 Dec 2009, 07:19
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

Kudos [?]: 540 [0], given: 6

Manager
Joined: 13 Oct 2009
Posts: 116

Kudos [?]: 101 [0], given: 66

Location: USA
Schools: IU KSB
Re: Bacteria Population, Area of Triangle [#permalink]

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16 Dec 2009, 07:35
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.

Kudos [?]: 101 [0], given: 66

Math Forum Moderator
Joined: 02 Aug 2009
Posts: 4969

Kudos [?]: 5465 [0], given: 112

Re: Bacteria Population, Area of Triangle [#permalink]

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16 Dec 2009, 07:41
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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Absolute modulus :http://gmatclub.com/forum/absolute-modulus-a-better-understanding-210849.html#p1622372
Combination of similar and dissimilar things : http://gmatclub.com/forum/topic215915.html

Kudos [?]: 5465 [0], given: 112

Re: Bacteria Population, Area of Triangle   [#permalink] 16 Dec 2009, 07:41
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