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Question

# Co-ordinates of vertices of a triangle are (0,0),(0,21) and (21,0). How many points with integral coordinates lie inside this triangle?

A
190
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B
250
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C
200
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D
201
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Solution

## The correct option is B 190The line joining the given points are x=0, y=0, x+y=21Any point lying inside the triangle formed by these lines must follow the below conditions :x>0, y>0, x+y−21<0Let x=1 ⇒0<y<20 i.e, 19 points x=2 ⇒0<y<19 i.e, 18 points x=19 ⇒0<y<2 i.e, 1 points∴ Total =19+18+........+1 =19×202⇒ Total =190Hence, the answer is 190.

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