Problem: points a , b , and , c have xy - coordinates ( 20 ) , ( 812 ) , and ( 140 ) , respectively . points x , y , and z have xy - coordinates ( 60 ) , ( 84 ) , and ( 100 ) , respectively . what fraction c of the area of triangle abc is the area of triangle xyz ?
Rationale: if you notice , both triangles abc and xyz have a side on x axis . we can take these sides as bases for each triangle , therefore area of abc is 1 / 2 * 12 * 12 ( height of abc is the y coordinate of the third point ( 812 ) ) similarly area of xyz is 1 / 2 * 4 * 4 dividing area of xyz with that of abc gives c = 1 / 9 . a
annotated_formula: divide(divide(multiply(const_4, const_4), const_2), multiply(subtract(20, multiply(const_4, const_2)), divide(subtract(20, multiply(const_4, const_2)), const_2)))