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Re: Coordinate Circle [#permalink]
27 Jun 2008, 08:14

x^2+y^2=5 , so it is a circle with (0,0) as its orgin, with radius equal to 5^0.5 = 2.2 approx.

The 4 vertix (typo?) of the circles are exactly the 4 intercepts with the x-, y- axis.

So the 4 vertix are (2.2,0), (0,-2.2), (-2.2,0), and (0,2.2)

Let's go through the circumference, starting from (2.2,0), in clockwise direction: the first point on the circumference with integer coordinates is: (2,-1) (1,-2) (-1,-2) (-2,-1) (-2,1) (-1,2) (1,2) (2,1)

Re: Coordinate Circle [#permalink]
27 Jun 2008, 19:43

judokan wrote:

x^2+y^2=5 , so it is a circle with (0,0) as its orgin, with radius equal to 5^0.5 = 2.2 approx.

The 4 vertix (typo?) of the circles are exactly the 4 intercepts with the x-, y- axis.

So the 4 vertix are (2.2,0), (0,-2.2), (-2.2,0), and (0,2.2)

Let's go through the circumference, starting from (2.2,0), in clockwise direction: the first point on the circumference with integer coordinates is: (2,-1) (1,-2) (-1,-2) (-2,-1) (-2,1) (-1,2) (1,2) (2,1)

Answer is 8C)

Sorry, I overlook the question, it is concern about semi-circle.

My answer would be 4 (A) (2,-1) (1,-2) (-1,-2) (-2,-1)

Re: Coordinate Circle [#permalink]
22 Jul 2008, 02:56

fresinha12 wrote:

How many points on the circumference of a semi-circle represented with x^2+y^2=5 have integer coordinates? (A) 4 (B) 6 (C) 8 (D) 12 (E) 16

just thought i'd present a lil twist to a problem ritula posted

I have an issue with your problem. As long as the diameter of the semi-circle is parallel to an axis, the answer is 4, but it is possible to define semi-circles centered on the origin that pass through 5 integer coordinates ( e.g. m = -1/2 ).

Re: Coordinate Circle [#permalink]
22 Jul 2008, 04:38

Permuteer wrote:

fresinha12 wrote:

How many points on the circumference of a semi-circle represented with x^2+y^2=5 have integer coordinates? (A) 4 (B) 6 (C) 8 (D) 12 (E) 16

just thought i'd present a lil twist to a problem ritula posted

I have an issue with your problem. As long as the diameter of the semi-circle is parallel to an axis, the answer is 4, but it is possible to define semi-circles centered on the origin that pass through 5 integer coordinates ( e.g. m = -1/2 ).

But 5 is not a given option. Unless you want to pass the question, u have to take the one that makes most sense.

An interesting approach. I interpreted the "circumference of a semi-circle" as referring only to the curved part of the figure. I wonder if there is a rule for it. Still, wouldn't your interpretation yield nine points when (0,0) is counted?

Re: Coordinate Circle [#permalink]
22 Jul 2008, 07:44

I would have never caught the semi-circle catch in the question but yeah agree with you that answer should be 4. with 8c4 = 70 different possibilities..

Re: Coordinate Circle [#permalink]
22 Jul 2008, 08:54

Permuteer wrote:

I have an issue with your problem. As long as the diameter of the semi-circle is parallel to an axis, the answer is 4, but it is possible to define semi-circles centered on the origin that pass through 5 integer coordinates ( e.g. m = -1/2 ).

Re: Coordinate Circle [#permalink]
22 Jul 2008, 17:12

sset009 wrote:

Permuteer wrote:

I have an issue with your problem. As long as the diameter of the semi-circle is parallel to an axis, the answer is 4, but it is possible to define semi-circles centered on the origin that pass through 5 integer coordinates ( e.g. m = -1/2 ).

could you expand on that? what is m?

"m" is the common abbreviation for slope.

1) plot all eight answers for the original equation 2) draw circle through all eight points. 3) draw a line from (-2,1) to (2,-1). This line will pass through the origin and will have a slope of -1/2. 4) consider this line the diameter of the semi-circle. 5) the semi circle now passes through 5 points: (-2,1) (-1,2) (1,2) (2,1) (2,-1)

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