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DS Question

by GPS » Sat Jan 02, 2010 11:33 am
Hi

was grappling with this question,

Q. The vertices of a triangle are located at points :(-2,1),(3,1),(x,y) on a coordinate plane. What is the area of the triangle ?

(1) I y-1 I = 1
(2) the interior angle at vertex (x,y), measures 90°


can someone explain the reasons for the answer ? A
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Source: — Data Sufficiency |
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by raviraushanjha » Sat Jan 02, 2010 7:19 pm
IMO C is the Answer.

From the first we get the value of y which can be either y = 2 or 0 hence insufficient.

From two we get the interior angle at vertex is 90 degrees. Again insufficient.

Now combining the two.

As we know that the internal angle at the vertex is 90 degree and slopes of perpendicular lines are negative of the inverse. m=-(1/m1).

(1-y)/(3-x) = -(1/((1-y)/(-2-x))

1-y/3-x = 2+x/1-y
(1-y)^2 = (2+x)(3-x)i
substituting y either 0 or 2 we will get the LHS as == 1
solving the same we will get x as -2, 3. thus we can calculate the height. and thus tha area.


regards
Rav
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