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 integers that satisfy the inequalities -4 <= x <= 5 and 6<=y<=16. How many different triangles with these properties could be constructed?
110
1100
9900
10000
12100
#248
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- cans
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- galaxian
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X coordinate can have a total of : 5 - (-4) + 1 = 10 coordinates [+1 coz both inclusive]
Y ...................................: 16 - 6 + 1 = 11 Coordinates
So for any X & Y coordinate to lie in this range, we have this possibility :
10C2 * 11C2
Since, X coordinate of P = X coordinate of R.
Similarly, Y coordinate of P = Y coordinate of Q. [As PR is parallel to X Axis & PQ parallel to Y Axis]
We have a total of 4 x & y coordinates with us to be placed.
Hence, 10C2 * 11C2 * 4 = 9900
So OA should be C
Y ...................................: 16 - 6 + 1 = 11 Coordinates
So for any X & Y coordinate to lie in this range, we have this possibility :
10C2 * 11C2
Since, X coordinate of P = X coordinate of R.
Similarly, Y coordinate of P = Y coordinate of Q. [As PR is parallel to X Axis & PQ parallel to Y Axis]
We have a total of 4 x & y coordinates with us to be placed.
Hence, 10C2 * 11C2 * 4 = 9900
So OA should be C