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## GMAT - Problem Solving - Coordinate geometry

### 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 differ

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

Number of ways of choosing coordinates of point P = number of ways of choosing a line with integral x coordinate between -4 and 5 * number of ways of choosing a line with integral y coordinate between 6 and 16 = 11*10 = 110

Since PR is parellel to x axis, y coordinate of R = y coordinate of P

Number of ways of choosing x coordinate of R = 9

Similarly number of ways of choosing y coordinate of Q = 10

Total number of ways of making a triangle = 110*9*10 = 9900

C is correct