Solution:
Let’s draw a diagram to analyze the question:
Attachment:
image1.PNG [ 17.14 KiB | Viewed 16309 times ]
Right angled triangle ABC, right angled at A, satisfying the following conditions:
-3 ≤x1, x2≤ 5 and 2 ≤y1, y2≤ 11
Let the x and y coordinates for vertex A = (x1 and y1)
Let the x and y coordinates for vertex B = (x1 and y2) [As AB is parallel to Y Axis, “x” coordinate will be same as the vertex A only “Y” coordinate will change.]
Let the x and y coordinates for vertex C = (x2 and y1) [As AC is parallel to X Axis, “y” coordinate will be same as the vertex A only “X” coordinate will change.]
So, as the diagram represents the number of triangles with the given conditions will vary as x1 and x2’s and y1 and y2’s vary.
The total number of possibilities of triangles = x1 ×x2 ×y1 ×y2
= 9C1 8C1 10C1 9C1
= 6480
The correct answer option is “B”