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In the xy plane, the distance between the origin and the point (4,5)

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In the xy plane, the distance between the origin and the point (4,5) [#permalink] New post   20 Apr 2020, 11:37
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In the xy plane, the distance between the origin and the point (4,5) is the same as the distance between which of the following two points?

(A) (−3,2) and (−7,8)
(B) (−2,1) and (3,5)
(C) (-2,-4) and (1,0)
(D) (3,2) and (8,7)
(E) (4,1) and (-1,-4)

PS68850.02
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Re: In the xy plane, the distance between the origin and the point (4,5) [#permalink] New post   20 Apr 2020, 11:42
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Distance between (0,0) and (4,5)= \(\sqrt{(4-0)^2+(5-0)^2}\) = \(\sqrt{4^2+5^2}\)

Option A - Distance between (−3,2) and (−7,8) = \(\sqrt{(-7+3)^2+(8-2)^2}\) = \(\sqrt{4^2+6^2}\) {rejected}

Option B - Distance between (−2,1) and (3,5) = \(\sqrt{(3-(-2))^2+(5-1)^2}\) = \(\sqrt{5^2+4^2}\) {Answer}

We don't have to check further


Bunuel wrote:
In the xy plane, the distance between the origin and the point (4,5) is the same as the distance between which of the following two points?

(A) (−3,2) and (−7,8)
(B) (−2,1) and (3,5)
(C) (-2,-4) and (1,0)
(D) (3,2) and (8,7)
(E) (4,1) and (-1,-4)

PS68850.02
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In the xy plane, the distance between the origin and the point (4,5) [#permalink] New post   20 May 2020, 19:54
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gmatt1476 wrote:
In the xy plane, the distance between the origin and the point (4,5) is the same as the distance between which of the following two points?

(A) (−3,2) and (−7,8)
(B) (−2,1) and (3,5)
(C) (-2,-4) and (1,0)
(D) (3,2) and (8,7)
(E) (4,1) and (-1,-4)


Step 1: Find the distance between the origin (0,0) and (4,5)

\(\sqrt{4^2 + 5^2}\) = \(\sqrt{41}\)

Step 2: Scan the answer choices to see if any of the two points have a distance of 4 and 5 respectively on the x or y axis.

(B) -2 and 3 have a distance of 5 on the x axis. 1 and 5 have a distance of 4 on the y axis. Therefore the distance between (-2,1) and (3,5) is \(\sqrt{41}\)
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Re: In the xy plane, the distance between the origin and the point (4,5) [#permalink] New post   30 May 2020, 08:06
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We the distance between the origin and the point (x, y) = \(x^{2} + y^{2}\)

so the distance from (0, 0) to (4, 5) = \(\sqrt{4^{2} + 5^{2}}\) = \(\sqrt{41}\)

Option A : The distance between (-3, 2) and (-7, 8) = \(\sqrt{100}\) = 10 Not Matching

Option B : The distance between (-2, 1) and (3, 5) = \(\sqrt{4^{2} + 5^{2}}\) = \(\sqrt{41}\) Matching


Therefore answer is Option B
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Re: In the xy plane, the distance between the origin and the point (4,5) [#permalink] New post   11 Feb 2021, 08:42
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SOLUTION:

A NEW OG 2021 QUESTION

First, find the distance between (4,5) representing (x1,y1) and (0,0) representing (x2,y2) using the distance formula

(Distance b/w (x1,y1) and (x2,y2) ) = √(x2-x1)^2 + (y2-y1)^2 )

=√(4-0)^2 + (5-0)^2 = √4^2+ 5^2

=√41

Now check the options

Option A - Distance b/w (−3,2) and (−7,8) using the distance formula = √(−7+3)^2+(8−2)^2

= √(-4)^2 + (6)^2 = √16 + 36 and is not equal to √41

Option B- Distance b/w (−2,1) and (3,5) using the distance formula = √(3−(−2))^2+(5−1)^2

= √25+16 = √41 and is EQUAL to the distance b/w points (4,5) and (0,0) as calculated above.

OPTION(B)
Hope this answers :thumbsup:
Devmitra Sen(Math)
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Re: In the xy plane, the distance between the origin and the point (4,5) [#permalink] New post   15 May 2021, 04:23
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gmatt1476 wrote:
In the xy plane, the distance between the origin and the point (4,5) is the same as the distance between which of the following two points?

(A) (−3,2) and (−7,8)
(B) (−2,1) and (3,5)
(C) (-2,-4) and (1,0)
(D) (3,2) and (8,7)
(E) (4,1) and (-1,-4)

PS68850.02


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Answer: Option B

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Re: In the xy plane, the distance between the origin and the point (4,5) [#permalink] New post   12 Jun 2022, 23:35
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gmatt1476 wrote:
In the xy plane, the distance between the origin and the point (4,5) is the same as the distance between which of the following two points?

(A) (−3,2) and (−7,8)
(B) (−2,1) and (3,5)
(C) (-2,-4) and (1,0)
(D) (3,2) and (8,7)
(E) (4,1) and (-1,-4)

PS68850.02


The question stem and answer choices all have integer values that are pretty small. In the stem, we go over 4 and up 5. Let's just glance at the answer choices to see if any have some combination of up/over 4/5.

A) Over 4 up 6. Nope.
B) Over 5 up 4. Yep

Answer choice B.

I strongly recommend on coordinate geometry questions holding off on doing the "real" math until you've given yourself maybe 20 seconds to see if you can get the right answer without it. By my count, you can ~75% of the time regardless of difficulty level.
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Re: In the xy plane, the distance between the origin and the point (4,5) [#permalink] New post   10 Mar 2023, 14:00
I have solved this question quite differently.

If we were to draw a line between the origin and the point (4,5), that line will have a slope of 4/5.

Then I checked a mong the answer choices which two points will make a line that has the same slope. I calculated the slope of each line and it turned out that the slope of the line created by the points in answer choice B (-2,1) and (3,5) has a slope of 4/5--> m=5-1/3-(-2)=4/5.


Bunuel TargetTestPrep Abhishek009 Can you please confirm if this method is correct?
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In the xy plane, the distance between the origin and the point (4,5) [#permalink] New post   10 Mar 2023, 14:20
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HoudaSR wrote:
I have solved this question quite differently.

If we were to draw a line between the origin and the point (4,5), that line will have a slope of 4/5.

Then I checked a mong the answer choices which two points will make a line that has the same slope. I calculated the slope of each line and it turned out that the slope of the line created by the points in answer choice B (-2,1) and (3,5) has a slope of 4/5--> m=5-1/3-(-2)=4/5.


Bunuel TargetTestPrep Abhishek009 Can you please confirm if this method is correct?


HoudaSR

I do not agree with your approach. Slope tells you the DIRECTION from one point to another, but not the distance, while the question is about DISTANCE. What if one of the answer choices had been (-2,1) and (8,9)? That would pass your test, but is clearly much farther away (twice as far, in fact).
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Re: In the xy plane, the distance between the origin and the point (4,5) [#permalink] New post   10 Mar 2023, 14:29
ThatDudeKnows wrote:
HoudaSR wrote:
I have solved this question quite differently.

If we were to draw a line between the origin and the point (4,5), that line will have a slope of 4/5.

Then I checked a mong the answer choices which two points will make a line that has the same slope. I calculated the slope of each line and it turned out that the slope of the line created by the points in answer choice B (-2,1) and (3,5) has a slope of 4/5--> m=5-1/3-(-2)=4/5.


Bunuel TargetTestPrep Abhishek009 Can you please confirm if this method is correct?


HoudaSR

I do not agree with your approach. Slope tells you the DIRECTION from one point to another, but not the distance, while the question is about DISTANCE. What if one of the answer choices had been (-2,1) and (8,9)? That would pass your test, but is clearly much farther away (twice as far, in fact).



It makes sense. Thank you for the example given.
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Re: In the xy plane, the distance between the origin and the point (4,5) [#permalink] New post   01 Jun 2023, 16:26
What if i used the mid point method, that seems to work perfectly well and is the most efficient way to solve this question.

ThatDudeKnows wrote:
gmatt1476 wrote:
In the xy plane, the distance between the origin and the point (4,5) is the same as the distance between which of the following two points?

(A) (−3,2) and (−7,8)
(B) (−2,1) and (3,5)
(C) (-2,-4) and (1,0)
(D) (3,2) and (8,7)
(E) (4,1) and (-1,-4)

PS68850.02


The question stem and answer choices all have integer values that are pretty small. In the stem, we go over 4 and up 5. Let's just glance at the answer choices to see if any have some combination of up/over 4/5.

A) Over 4 up 6. Nope.
B) Over 5 up 4. Yep

Answer choice B.

I strongly recommend on coordinate geometry questions holding off on doing the "real" math until you've given yourself maybe 20 seconds to see if you can get the right answer without it. By my count, you can ~75% of the time regardless of difficulty level.
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Re: In the xy plane, the distance between the origin and the point (4,5) [#permalink]
01 Jun 2023, 16:26
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