The line y=31x+1 divides the square region defined by 0≤x≤2 and 0≤y≤2 into an upper and a lower region. The line x=a divides the lower region into two regions of equal area. Then a can be written as s−t, where s and t are positive integers. What is s+t?
Answer Choices:
A. 18
B. 19
C. 20
D. 21
E. 22
💬 Join the Discussion
Stuck on this problem or want to share your approach?
Continue the conversation and see what others are thinking: View Forum Thread
Take a look at the diagram above, and assign coordinates to the vertices as shown. Note that E is the point on ℓ:y=31x+1 when x=0, or (0,1), and F is the point on ℓ when x=2, or (2,35). Note that the x-coordinate of I is a, so
I=(a,3a+1)
The blue line x=a splits quadrilateral AEFB in equal portions, so [AEIG]=[GIFB]. Note both of these are trapezoids - AEIG has bases AE,GI and height AG, while BGIF has bases BF,GI and height BG. Hence,
