sadd wrote:

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 be integers that satisfy the inequalities -4 <= x <= 5 and 6<= y<= 16. How many different triangles with these properties could be constructed?

(A) 110

(B) 1,100

(C) 9,900

(D) 10,000

(E) 12,100

What is the right choice?

OA: C

Given :\(-4 <= x <= 5;6<= y<= 16\)

As given PR is parallel to x axis

for \(y=6\), We have \(10\) \((-4 <= x <= 5)\) options for selecting \(R\), Then \(9\) (\(-4 <= x <= 5\)minus one,which is already selected for \(R\)) options available for selecting \(P\) and for \(Q\) we have \(10\) ( \(6<= y<= 16\) minus \(y=6\) otherwise all \(3\) point will be collinear)

Attachment:

triangle possibility.PNG [ 20.21 KiB | Viewed 376 times ]
Total triangle for \(y=6 : 9*10*10 =900 triangles\)

Similarily

for y \(=7 : 900\) triangles

for y \(=8 : 900\) triangles

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.

.

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for y \(=16 : 900\) triangles

Total triangle \(= (16-6+1)*900 =9900\)

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