raajan_p wrote:If c > 0 and d > 0, then which of the following expressions is the area enclosed by the line with the equation x = 0, the line with the equation y = 0, and the line with the equation y = cx + d ?
A) d/2c
B) d^2/2c
C) d^2/c
D) c^2/2d
E) cd/2
If we're not sure about the algebra, we can attack this question by picking numbers instead.
Let's let our equation be y = 2x + 6
so, we've chosen:
c = 2
d = 6
If we draw out our triangle, we see that the 3 vertices are at (0,0), (0,6) and (-3,0), giving us a base of 3 and a height of 6.
area = 1/2(b)(h) = 1/2(3)(6) = 9
Now we plug our values for c and d into the choices:
(a) 6/4... wrong
(b) 36/4 = 9... right
(c) 36/2... wrong
(d) 4/12... wrong
(e) 12/2... wrong
Only (b) worked out, therefore (b) is correct!
If more than 1 choice worked (for example, if we had picked c=2 and d=4, both (b) and (e) work), then we'd have to try another set of numbers, only checking the choices we haven't been able to eliminate. As a general rule, the stranger the numbers you choose, the less likely it is that you'll get duplicates.
If you like algebra, jimmiejaz's solution is great.
