A vertical line divides the triangle with vertices (0,0), (1,1) and (9,1) in the *xy*-plane into two regions of equal area. What is the equation of the line?

*x*= 2.5*x*= 3.0*x*= 3.5*x*= 4.0*x*= 4.5

The area of △

*OBD*is split in half by line*CA*. △*OBD*has base*BD*= 8 and altitude*EO*= 1. So area △*OBD*= (8 x 1)/2 = 4. This means area △*ABC*= 2 =*a*(*CA*)/2.We know

*CA*||*OE*, so △*BAC*∼ △*BOE*, and*CA/OE = BC/BE*, i.e.,*CA*/1 =*a*/9.Now area △

*ABC*=*a*(*CA*)/2 = (*a*)(*a*)/(2)(9) =*a*^{2}/18 and this area is 2. But*a*^{2}/18 = 2 →*a*= 6.Thus line

*CA*intersects the*x*-axis at*x*=3, and that’s the equation of line*CA*:*x*= 3.The answer is (b).

so what is the equation?

so what ths equation?