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

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In the coordinate plane, what is the distance between points (3, 5) an [#permalink]

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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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Re: In the coordinate plane, what is the distance between points (3, 5) an [#permalink]

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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]

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New post 21 Feb 2016, 22:26
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]

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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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Re: In the coordinate plane, what is the distance between points (3, 5) an [#permalink]

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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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In the coordinate plane, what is the distance between points (3, 5) an [#permalink]

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New post 23 Feb 2016, 02:41
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. \(\sqrt{41}\)



Kudos for correct solution.


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]

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New post 14 Jul 2016, 08:05
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. \(\sqrt{41}\)



Kudos for correct solution.


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]

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New post 06 Nov 2017, 09:43
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. \(\sqrt{41}\)

Kudos for correct solution.

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]

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New post 08 Nov 2017, 17:29
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] 08 Nov 2017, 17:29
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