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In the xyplane, which of the following points is the greatest distanc [#permalink]
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13 Dec 2017, 08:39
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In the xyplane, which of the following points is the greatest distanc [#permalink]
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13 Dec 2017, 09:23
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Bunuel wrote: In the xyplane, which of the following points is the greatest distance from the origin?
(A) (0,3) (B) (1,3) (C) (2,1) (D) (2,3) (E) (3,0) Points on the axes lie on the same line as the origin, and have the same x or ycoordinates. Subtract 0 from the nonzero coordinate. For other points, you could construct a right triangle with horizontal and vertical legs that = length of coordinates. (A) (0,3) From ycoordinates of (0,3) and (0, 0) Distance \(= (3  0) = 3\) (B) (1,3) Distance, d, from a right triangle with leg = 1 and leg = 3 (Pythagorean theorem): \((1^2 + 3^2) = d^2\) \((1 + 9) = 10 = d^2\) Distance \(= \sqrt{10}\) (C) (2,1) Distance, d, from a right triangle: \((2^2 + 1^2) = (4 + 1) = 5 = d^2\) Distance \(= \sqrt{5}\) (D) (2,3) Distance, d, from a right triangle: \((2^2 + 3^2) = (4 + 9) = 13 = d^2\) Distance \(= \sqrt{13}\) (E) (3,0) From xcoordinates of (3,0) and (0,0) Distance \(= (3  0) = 3\) Answer D
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Re: In the xyplane, which of the following points is the greatest distanc [#permalink]
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13 Dec 2017, 22:37
D it is Use the Pythagorean theorem and put values of x and y x^2 + y^2 = c^2 the option that has highest value of C is the answer
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Re: In the xyplane, which of the following points is the greatest distanc [#permalink]
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14 Feb 2018, 11:58
generis wrote: Bunuel wrote: In the xyplane, which of the following points is the greatest distance from the origin?
(A) (0,3) (B) (1,3) (C) (2,1) (D) (2,3) (E) (3,0) Points on the axes lie on the same line as the origin, and have the same x or ycoordinates. Subtract 0 from the nonzero coordinate. For other points, you could construct a right triangle with horizontal and vertical legs that = length of coordinates. (A) (0,3) From ycoordinates of (0,3) and (0, 0) Distance \(= (3  0) = 3\) (B) (1,3) Distance, d, from a right triangle with leg = 1 and leg = 3 (Pythagorean theorem): \((1^2 + 3^2) = d^2\) \((1 + 9) = 10 = d^2\) Distance \(= \sqrt{10}\) (C) (2,1) Distance, d, from a right triangle: \((2^2 + 1^2) = (4 + 1) = 5 = d^2\) Distance \(= \sqrt{5}\) (D) (2,3) Distance, d, from a right triangle: \((2^2 + 3^2) = (4 + 9) = 13 = d^2\) Distance \(= \sqrt{13}\) (E) (3,0) From xcoordinates of (3,0) and (0,0) Distance \(= (3  0) = 3\) Answer D Hi generis its me again i have a question why didnt you put options A and E under radical sign square it (E) (3,0) From xcoordinates of (3,0) and (0,0) Distance \(=\sqrt{(3  0)^2}= 3\) the applies for option A no ? merci beaucoup



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In the xyplane, which of the following points is the greatest distanc [#permalink]
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14 Feb 2018, 19:47
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dave13 wrote: generis wrote: Bunuel wrote: In the xyplane, which of the following points is the greatest distance from the origin?
(A) (0,3) (B) (1,3) (C) (2,1) (D) (2,3) (E) (3,0) Points on the axes lie on the same line as the origin, and have the same x or ycoordinates. Subtract 0 from the nonzero coordinate. For other points, you could construct a right triangle with horizontal and vertical legs that = length of coordinates. (A) (0,3) From ycoordinates of (0,3) and (0, 0) Distance \(= (3  0) = 3\) (B) (1,3) Distance, d, from a right triangle with leg = 1 and leg = 3 (Pythagorean theorem): \((1^2 + 3^2) = d^2\) \((1 + 9) = 10 = d^2\) Distance \(= \sqrt{10}\) (C) (2,1) Distance, d, from a right triangle: \((2^2 + 1^2) = (4 + 1) = 5 = d^2\) Distance \(= \sqrt{5}\) (D) (2,3) Distance, d, from a right triangle: \((2^2 + 3^2) = (4 + 9) = 13 = d^2\) Distance \(= \sqrt{13}\) (E) (3,0) From xcoordinates of (3,0) and (0,0) Distance \(= (3  0) = 3\) Answer D Hi generis its me again i have a question why didnt you put options A and E under radical sign square it (E) (3,0) From xcoordinates of (3,0) and (0,0) Distance \(=\sqrt{(3  0)^2}= 3\) the applies for option A no ? merci beaucoup dave13 , you are correct. You could use the distance formula for A and E. I am not positive that is the question you ask. Your "distance" for E seems to leave out part of the distance formula. If it IS supposed to be the distance formula, I think it should say: \(=\sqrt{(3  0)^2 + (0  0)^2}= 3\) Three comments. 1) I neither like nor use the distance formula, described as "the Pythagorean theorem in disguise." I am happy with the unconcealed version. So I draw right triangles and use the Pythagorean theorem to find or compare distances. 2) if you work well with the distance formula, use it! 3) regarding A and E, I will restate less cryptically than above: "Points [that lie] on the [x or y] axes lie on the same line as [points on] the origin, and have [either] the same x or [the same] ycoordinates. Subtract 0 from the nonzero coordinate." Answer A's "two" points, (0,0) and (0,3), lie on the yaxis. Their xcoordinates = 0. Graph it. There is no need for the distance formula (or my right triangles). The distance of point (0,3) to origin (0,0)? \(y_2  y_1 = 3\)Answer E's two points lie on the xaxis. Same analysis, except the ycoordinates = 0. Subtract xcoordinates. But if the distance formula is your goto, again: use whatever works for you. There is a saying in the U.S. (poor grammar, do not use in SC!): If it ain't broke, don't fix it. De rien
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In the xyplane, which of the following points is the greatest distanc
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