Coordinate Geometry

[Tdot23]

Hi BTG Community,
I'm attaching a picture of the question from the Princeton 1012. I am having hard time understanding their answer key so would love to get a different view.. Thanks! Hope you can make out the question...

[hey_thr67]

Not able to see the problem completely..

[massi2884]

Could you please type the question?
Thanks.

[Tdot23]

My Apologies for that. The question reads as follows:

In the rectangular coordinate system above (its a picture of a triangle ABC where AC lies on the X asis, B is the "top" or the 3rd vertex), if AB < BC, is the area of region ABC less than 45?

(1)The coordinates of point B are (5, 12)
(2) The coordiantes of point C are (15, 0)

The answer is A according to the answer key, but difficult to follow... Thanks again.

[Anurag@Gurome]

In the rectangular coordinate system above (its a picture of a triangle ABC where AC lies on the X axis, B is the "top" or the 3rd vertex) and A is at the origin, if AB < BC, is the area of region ABC less than 45?

(1)The coordinates of point B are (5, 12)
(2) The coordinates of point C are (15, 0)

The diagram is as follows


Note that y-coordinate of B is the height of the triangle and x-coordinate of C is the length of the base of the triangle.

Statement 1: If AB was equal to BC, then coordinates of C would have been (10, 0). In that case area of ABC would have been = (base)*(height)/2 = (10*12)/2 = 60 > 45

As BC > AB, x-coordinate of C is more than 10. Hence, area of the triangle is definitely more than 60 which is greater than 45.

Sufficient

Statement 2: Are of the triangle will depend upon the y-coordinate of B.

Not sufficient

The correct answer is A.

[hey_thr67]

To me answer is A. It is because, AB comes out to be 13 . Consider a perpendicular to base AC intersecting at D.

5^2 + 12^2 = 13^2.

Now BC is greater than AB so lets lake minimum value of BC. which is 13. So, base to be minimum 10. Now calculating area of the triangle it is minimum 60. Hence it is greater than 45. So A is the answer.

[hey_thr67]

To me answer is A. It is because, AB comes out to be 13 . Consider a perpendicular to base AC intersecting at D.

5^2 + 12^2 = 13^2.

Now BC is greater than AB so lets lake minimum value of BC. which is 13. So, base to be minimum 10. Now calculating area of the triangle it is minimum 60. Hence it is greater than 45. So A is the answer.