ds: Triangle Area

Question

easy one <img src="{SMILIES_PATH}/1f602.png" class="forumSmileyItem" width="20" height="20" alt=":lol:" title="Laughing" />

kapslock · Answer

The two points that are the two vertices of the triangle are (-2, 2) and (3, 2).

They lie on a horizontal line parallel to the x axis.

1. |y-2| = 1
=> y = 1 or -3. This is a line parallel to x axis. Since the area of a triangle is constant when the third of its vertices lies  anywhere  on a line parallel to its base, its area can be determined. Therefore sufficient.

2. The angle at the vertex x, y is 90 degrees. This just means the vertex x, y lies on a circle whose diameter is the points (-2, 2) and (3, 2).

This does not give a constant area, and so with this information, we cannot determine the area of the triangle. Hence insufficient.

Therefore, (A).

mirhaque · Answer

excillent <img src="{SMILIES_PATH}/1done.gif" alt=":done" title="Done" /> <img src="{SMILIES_PATH}/1ole.gif" alt=":wave" title="Wave" />

christoph · Answer

ok. in dont get this one. how can the area be determinded when the height in 1) is different 1 or -3 ? wouldnt the triangle be smaller in case of 1 or bigger in case of -3 ?

banerjeea_98 · Answer

nope in state 1, y can be 1 or 3....but in each case the distance from the line (-2,2) and (3,2) remains the same i.e. 1

christoph · Answer

thx, baner ! it should be 3 and not -3 !

kwasi7 · Answer

Interesting ques. the kind i'd like to see on test day. :cool 

One just has to be quick not to conclude that since Y has 2 values the statement cannot be sufficient.

thanks

ds: Triangle Area

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