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A right angled triangle GHI is to be formed in a rectangular coordinat

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A right angled triangle GHI is to be formed in a rectangular coordinat  [#permalink]

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New post Updated on: 20 Oct 2016, 08:29
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A right angled triangle GHI is to be formed in a rectangular coordinate system such that the triangle is right angled at H and HI is parallel to the Y axis. It is also intended for the x and the y coordinates of G, H and I to satisfy the following inequalities. x must lie between -8 and 8 (both inclusive) and y must lie between 7 and 15 (both inclusive). How many such triangles can be formed?

(A) 78
(B) 1224
(C) 19584
(D) 20566
(E) 30126

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Originally posted by shubhraghosh on 20 Oct 2016, 08:26.
Last edited by Bunuel on 20 Oct 2016, 08:29, edited 1 time in total.
Renamed the topic.
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Re: A right angled triangle GHI is to be formed in a rectangular coordinat  [#permalink]

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New post 20 Oct 2016, 08:33
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shubhraghosh wrote:
A right angled triangle GHI is to be formed in a rectangular coordinate system such that the triangle is right angled at H and HI is parallel to the Y axis. It is also intended for the x and the y coordinates of G, H and I to satisfy the following inequalities. x must lie between -8 and 8 (both inclusive) and y must lie between 7 and 15 (both inclusive). How many such triangles can be formed?

(A) 78
(B) 1224
(C) 19584
(D) 20566
(E) 30126


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A right angled triangle GHI is to be formed in a rectangular coordinat  [#permalink]

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New post 13 May 2017, 22:57
First let's count the coordinates of H. H can take (8+8+1) points in a horizontal line. There are 9 horizontal lines in total inside the shaded rectangular grid.
So, H can take 17×9 points.
Now, I must be placed straight up or down to H to make HI parallel to y axis.
So, I can take (9-1) points.
Lastly, G should be in the same horizontal line as H since the triangle is right angled at H.
So, G can take (17-1) points.
Hence, total triangles= 17×9×8×16=19584.
However, the question should state that GHI can only take integer values.

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A right angled triangle GHI is to be formed in a rectangular coordinat &nbs [#permalink] 13 May 2017, 22:57
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