Olympiad workbookIOQMStraight Lines

Consider a square A B C D of side length 16 . Let E, F be points on C D such that C E=E F=F D . Let the line BF and A E meet in M . The area of M A B is:

Correct answer

Step-by-step solution

Eq of line A E: 2 y-3 x+16=0 Eq of line B F : 2 y+3 x-32=0 M (8,4) Area of triangle A M B aligned | 1 2 | array ccc 0 & 16 & 1 16 & 16 & 1 8 & 4 & 1 array | & = 1 2 (-16(8)+1(64-8 16)) & = | 1 2 (-16 16+64) | & = | 16 2 (4-16) |=8 12 & =96 sq.units aligned

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