The right angled 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 inequality −4≤x≤5 & 6≤y≤16. How many different triangles with these properties could be constructed?
A. 1,100 B. 12,100 C. 10,000 D. 9,900

• We have the rectangle with dimensions 10*11 (10 horizontal dots and 11 vertical). PQ is parallel to y-axis and PR is parallel to x-axis.
  
  Choose the (x,y) coordinates for vertex P (right angle): 10C1*11C1;
  Choose the x coordinate for vertex R (as y coordinate is fixed by A): 9C1, (10-1=9 as 1 horizontal dot is already occupied by A);
  Choose the y coordinate for vertex Q (as x coordinate is fixed by A): 10C1, (11-1=10 as 1 vertical dot is already occupied by A).
  
  10C1*11C1*9C1*10C1=9900.
  
  Answer: C.
• 6 years agoHelpfull: Yes(11) No(0)
• Ans 9900
  
  P can take a total of 10*11 co-ordinates(10 of x and 11 of y)
  
  For a given P, R can take a total of 9 co-ordinates and Q can take a total of 10 co-ordinates.
  
  Hence, total = 110*9*10 = 9900
• 6 years agoHelpfull: Yes(5) No(4)
• -4 to 5 = 10
  6 to 16 = 11
  10 * 11 * 90 = 9900
• 6 years agoHelpfull: Yes(4) No(0)
• a
  -4 to 5 is 10
  6 to 16 is 11
• 6 years agoHelpfull: Yes(1) No(1)
• P can take a total of 10*11 co-ordinates(10 of x and 11 of y)
  
  For a given P, R can take a total of 9 co-ordinates and Q can take a total of 10 co-ordinates.
  
  Hence, total = 110*9*10 = 9900
• 5 years agoHelpfull: Yes(1) No(0)
• my answer is 1100
• 5 years agoHelpfull: Yes(0) No(3)