Triangle in Coordiante plane

[arora007]

On the xy plane what is the area of a right triangle, one side of which is defined by the two points having the (x,y) coordinates (2,3) and (-4,0)?

1) The triangle crosses the y-axis at exactly two points.
2) The y coordinate of two of the triangle's three vertices is 0(zero)

OA is E, however i initially ran into the answer B

the above is from Peterson Master the GMAT TEST 1

[jonathan123456]

Hi,

Can you explain, how the answer is E?

from B:

If the vertice of the right triangle has co-ordinates where y=0, then the third point should be on x axis.
For a right triangle, it should be perpendicular to x axis , so there can be only 1 line, (starting from point (2,3) perpendicular to x axis), thus area can be found out.

/Jon

[arora007]

simple,
consider (2,3) as a right angle once this is first triangle
consdier (x,0) as the right angle .

you will have two triangle, both will have different co-ordinates,(x,0) hence a different area.

and hence the answer is E

[Haaress]

Arora007, I like your questions. Please keep them coming.

From stmt 2 , we have 2 right angle traingle: One with the coordinates - (-4,0) , (2,3) and (2,0) , and another with (-4,0) , (2,3) and (3.5, 0)....pm me if you need more explanation on the bolded set of coordinates. Thus B is insuff.

Stmt 1 is also insuff because there are 4 Right angle traingles fitting into the conditions of the stmt.

Hope that helps.

[gmatrant]

Given that two points , the y co-ord is 0 and also its a right angled triangle, so two lines must be perpendicularity.
(-4,0) , (2,3) and (3.5, 0) - how do these co-ord ensure perpendicularity?
Can you please explain?

[Haaress]

If you calculate the slope between the first 2 set of coordinates and that of the last two coordinated,the product is a negative one, which indicates the 2 lines. ate perpendicular.

I am responding to your question through my cell so I'll respond in a few hours off you still have some lingering questions Please excuse incase of misspellings. thanks