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800Score coordinate geometry question

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800Score coordinate geometry question

by varunkh70 » Thu Mar 05, 2009 3:51 pm
The vertices of a triangle are at coordinates (-2,1),(3,1),(x,y) on a plane. What is the area of the triangle?

(1) |y-1| = 1
(2) The angle at the vertex (x,y) is 90 degrees

Please help me with this. I feel the answer should be E but the given answer is A. Here, y has can have two values hence its not possible to clearly point out the right answer so i think the answer should be E
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by pakaskwa » Thu Mar 05, 2009 6:31 pm
If you draw the coordinate, it's easy to understand. First, draw a line between (-2,1) and (3,1). This is the base of the triangle, which is the distance between 3 and -2, that's 5.

Now we need to find the height of the triangle. From |y-1|=1, we know that possible values for y is either 2 or 0. Draw two lines, y=2 and y=0 (falls on axis x). These 2 lines are parallel to the first line we drew above. So the distance between them is always 1.

For the last vertex (x,y), it will always fall on those 2 lines. No matter where x is, height of the triangle is always 1.

Area of the triangle is 1/2 x 5 x 1 = 5/2.
Last edited by pakaskwa on Fri Mar 06, 2009 3:04 pm, edited 1 time in total.
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by kamu » Fri Mar 06, 2009 2:04 am
Small correction. The base is 5. 3-(-2) = 5.
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by pakaskwa » Fri Mar 06, 2009 3:05 pm
Oops, you are right Kamu. I fixed it in my posting so nobody will get confused...

Thanks!
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