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In the coordinate plane, what is the distance between points (3, 5) an

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Bunuel
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In the coordinate plane, what is the distance between points (3, 5) an [#permalink] New post   21 Feb 2016, 10:12
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In the coordinate plane, what is the distance between points (3, 5) and (7, 10)?

A. 3
B. 4
C. \(2\sqrt{5}\)
D. \(\sqrt{37}\)
E. \(\sqrt{41}\)



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E
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BrentGMATPrepNow
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In the coordinate plane, what is the distance between points (3, 5) an [#permalink] New post   Updated on: 22 Feb 2021, 06:31
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Bunuel wrote:
In the coordinate plane, what is the distance between points (3, 5) and (7, 10)?

A. 3
B. 4
C. \(2\sqrt{5}\)
D. \(\sqrt{37}\)
E. \(\sqrt{41}\)



Distance between \((a,b)\) and \((c,d)\) \(= \sqrt{(d-b)^2+(c-a)^2}\)

So, the distance between \((3, 5)\) and \((7, 10)\) \(= \sqrt{(10-5)^2+(7-3)^2}\)
\(= \sqrt{5^2+4^2}\)
\(= \sqrt{25+16}\)
\(= \sqrt{41}\)

Answer: E

Originally posted by BrentGMATPrepNow on 22 Feb 2016, 16:01.
Last edited by BrentGMATPrepNow on 22 Feb 2021, 06:31, edited 1 time in total.
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Re: In the coordinate plane, what is the distance between points (3, 5) an [#permalink] New post   21 Feb 2016, 11:43
Distance between (3, 5) and (7, 10)
= [ (7-3)^2 + (10-5)^2 ]^(1/2)
= [ 4^2 + 5^2 ]^(1/2)
= [41]^(1/2)

Answer E
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Re: In the coordinate plane, what is the distance between points (3, 5) an [#permalink] New post   21 Feb 2016, 22:26
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Distance between 2 points is [(x2-x1)^2 +(y2-y1)^2]^1/2

= [ (7-3)^2 + (10-5)^2 ]^(1/2)
= [ 4^2 + 5^2 ]^(1/2)
= [41]^(1/2)

Thus answer is E
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Re: In the coordinate plane, what is the distance between points (3, 5) an [#permalink] New post   22 Feb 2016, 01:01
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sqrt((y2-y1)^2 +(x2-x1)^2)
thus
sqrt((10-5)^2+(7-3)^2)
sqrt(25+16)= sqrt(41)

Ans:
E
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In the coordinate plane, what is the distance between points (3, 5) an [#permalink] New post   23 Feb 2016, 02:41
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Bunuel wrote:
In the coordinate plane, what is the distance between points (3, 5) and (7, 10)?

A. 3
B. 4
C. \(2\sqrt{5}\)
D. \(\sqrt{37}\)
E. \(\sqrt{41}\)



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Distance between two points = \(\sqrt{((x2 - x1)^2 + (y2 - y1)^2)}\)
In this particular case, \(\sqrt{((7-3)^2 + (10 - 5)^2 )}\)=\(\sqrt{(16 + 25)}\) = \(\sqrt{41}\)
Option E
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Re: In the coordinate plane, what is the distance between points (3, 5) an [#permalink] New post   14 Jul 2016, 08:05
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Bunuel wrote:
In the coordinate plane, what is the distance between points (3, 5) and (7, 10)?

A. 3
B. 4
C. \(2\sqrt{5}\)
D. \(\sqrt{37}\)
E. \(\sqrt{41}\)



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Use distance formula
\(d=\sqrt{(delta x)^2 +(delta y)^2}\)

\(d=\sqrt{(7-3)^2 +(10-5)^2}\)

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

\(d=\sqrt{(16)+(25)}\)

\(d=\sqrt{41}\)

Answer is E
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In the coordinate plane, what is the distance between points (3, 5) an [#permalink] New post   06 Nov 2017, 09:43
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Bunuel wrote:
In the coordinate plane, what is the distance between points (3, 5) and (7, 10)?

A. 3
B. 4
C. \(2\sqrt{5}\)
D. \(\sqrt{37}\)
E. \(\sqrt{41}\)

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Approach: One step away from the distance formula. For me, the latter is slower. This method = half a minute.

Find the leg lengths of the right triangle created by the two points (easy to see if you sketch). Hypotenuse = distance between points.

The length of one leg of the right triangle is the difference between the x-coordinates: (7-3) = 4

The length of the other leg is the difference between the y-coordinates: (10-5) = 5

Pythagorean theorem:
(leg 1)\(^2\) + (leg 2)\(^2\) = hypotenuse\(^2\) (= d\(^2\))

4\(^2\) + 5\(^2\) = d\(^2\)
16 + 25 = d\(^2\)
d\(^2\) = 41
d = \(\sqrt{41}\)

Answer E
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Re: In the coordinate plane, what is the distance between points (3, 5) an [#permalink] New post   08 Nov 2017, 17:29
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Bunuel wrote:
In the coordinate plane, what is the distance between points (3, 5) and (7, 10)?

A. 3
B. 4
C. \(2\sqrt{5}\)
D. \(\sqrt{37}\)
E. \(\sqrt{41}\)


We can use the distance formula:

d = √[(y2 - y1)^2 + (x2 - x1)^2]

d = √[(10 - 5)^2 + (7 - 3)^2]

d = √(5^2 + 4^2)

d = √(25 + 16) = √41

Answer: E
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Re: In the coordinate plane, what is the distance between points (3, 5) an [#permalink] New post   27 Jan 2020, 18:48
Correct Answer: E

The points (3, 5) and (7,10) will form a right triangle with sides of 4 (the difference in the x-coordinates, 7 - 3) and 5 (the difference in the y-coordinates, 10 -5). The hypotenuse is the distance between those two points.

Using the Pythagorean Theorem: 42+52=c2
; 16 + 25 = 41. c2
= 41, so c = 41−−√
. Note that A is a trap answer, encouraging you to see the sides of 4 and 5 and assume that this is a 3 - 4 - 5 right triangle. Because the distance between these points must be the hypotenuse, or longest side, that ratio is not true of this triangle.
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Re: In the coordinate plane, what is the distance between points (3, 5) an [#permalink] New post   22 Sep 2022, 05:19
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