Right triangle ABC is to be drawn in the xy-plane so that the right angle is at A and AB is parallel...
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 -7 ≤ x ≤ 1 and 4 ≤ y ≤ 9 , then how many different triangles can be drawn that will meet these conditions?
Answer/Solution
3024
Steps/Work
We have the rectangle with dimensions 9*7 (9 horizontal dots and 7 vertical). AB is parallel to y-axis and AC is parallel to x-axis.
Choose the (x,y) coordinates for vertex A: 9C1*7C1;
Choose the x coordinate for vertex C (as y coordinate is fixed by A): 8C1, (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): 6C1, (7-1=6 as 1 vertical dot is already occupied by A).
9C1*7C1*8C1*6C1=3024
Answer: D.
Choose the (x,y) coordinates for vertex A: 9C1*7C1;
Choose the x coordinate for vertex C (as y coordinate is fixed by A): 8C1, (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): 6C1, (7-1=6 as 1 vertical dot is already occupied by A).
9C1*7C1*8C1*6C1=3024
Answer: D.