right triangle abc is to be drawn in the xy - plane so that the right angle is at a and ab is parallel to the y - axis . if the x - and y - coordinates of a , b , and c are to be integers that are consistent with the inequalities - 3 ≤ x ≤ 2 and 4 ≤ y ≤ 9 , then how many different triangles can be drawn that will meet these conditions ?
"we have the rectangle with dimensions 9 * 3 ( 9 horizontal dots and 3 vertical ) . ab is parallel to y - axis and ac is parallel to x - axis . choose the ( x , y ) coordinates for vertex a : 9 c 1 * 3 c 1 ; choose the x coordinate for vertex c ( as y coordinate is fixed by a ) : 8 c 1 , ( 9 - 1 = 8 as 1 horizontal dot is already occupied by a ) ; choose the y coordinate for vertex b ( as x coordinate is fixed by a ) : 2 c 1 , ( 3 - 1 = 2 as 1 vertical dot is already occupied by a ) . 9 c 1 * 3 c 1 * 8 c 1 * 2 c 1 = 432 . answer : b ."
multiply(multiply(3, subtract(3, const_1)), multiply(9, 3))