Question

Right triangle PQR is to be constructed in the xy-plane so that the right angle is at P and PR is parallel to the x-axis. The x- and y-coordinates of P, Q, and R are to be integers that satisfy the inequalities -4 <= x <= 5 and 6<= y<= 16. How many different triangles with these properties could be constructed?
(A) 110
(B) 1,100
(C) 9,900
(D) 10,000
(E) 12,100

Answer 1

Answer:

(C) 9900

Step-by-step explanation:

The right triangle which right angle is at P and PR is parallel to the x-axis can have 4 sets (A,B,C,D as illustrated) of format depends on which direction is the right angle located.

each set have

(1+2+3+4+5+6+7+8+9) x (1+2+3+4+5+6+7+8+9+10) = 45 x 55 = 2475 right triangles

4 sets: 2475 x 4 = 9900