factor58 wrote:
would it be possible to provide a figure with the explanation please
factor58,
pattypatIt would be very difficult to provide eloborated figure but I hope this will help you to grab the concept!
To find out the number of terms (in case of inclusive), we can use the formulae = Last term - First term + 1
Since, \(-4 ≤ x ≤ 6\)
\(x = 6 - (-4) + 1\)
Number of possible values of \(x = 11\)
Also, \(7 ≤ y ≤ 15\)
\(y = 15 - 7 + 1\)
Number of possible values of \(y = 9\)
To costruct a right triangle - 2 points must have same x-coordinate (A and C) and 2 points must have same y-coordinate (A and B).
For example, in all Black triangles:The Vertical line AB has same x-coordinate as -4 and horizontal lines AC, AC', AC'', .... AC will have same y-coordinate as 7.
Number of ways of picking the x-coordinate of point A out of 11 possible options = \(^{11}C_1 = 11\)
Number of ways of picking the y-coordinate of point A out of 9 possible options = \(^{9}C_1 = 9\)
Since, we have already picked the x and y coordinates of point A - we will now have \(11 - 1 = 10\) possible options for the x-coordinate of point C and \(9 - 1 = 8\) possible options for the y-coordinate of point BFinally,
Number of ways of picking the x-coordinate of point C = \(^{10}C_1 = 10\)
NOTE: The y-coordinate of point C has to be same as that of Point A to form a Base (Horizontal line) i.e. \(7\)
And,
Number of ways of picking the y-coordinate of point B = \(^{8}C_1 = 8\)
NOTE: The x-coordinate of point B has to be same as that of Point A to form a Perpendicular (Vertictal line) i.e. \(-4\)
Total number of ways to form a right triangle = \((11)(9)(10)(8) = 7920\)
Col. A: \(7920\)
Col. B: \(8000\)
Col. A < Col. B
Hence, option B
Attachments
Right triangle ABC.png [ 21.36 KiB | Viewed 2141 times ]