The equation of a line is given as 4x+5y-8=0. Point A(7,4)and B(2,0) lie on the same line; and C(2,8). How to find the area of triangle ABC?

Answer 1

line AB has slope m=4/5. The intercept is B=y-mx = 0 - (4/5)(2) = -8/5.

So line AB has equation y = (4/5)x - 8/5

the 3rd side, IMPLIED by your statement in the problem passes through (2,8), so

the vertices are (-8,8) and (12,8), along with (2,0)

the height is from (2,0) to (2,8) = 8

and the base is from (-8,8) to (12,8) which is 20.

the area is then (1/2)*8*20 = 80