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

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Math Expert
Joined: 02 Sep 2009
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In the coordinate plane, what is the distance between points (3, 5) an  [#permalink]

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21 Feb 2016, 09:12
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Difficulty:

5% (low)

Question Stats:

91% (00:46) correct 9% (01:09) wrong based on 241 sessions

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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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21 Feb 2016, 10:43
Distance between (3, 5) and (7, 10)
= [ (7-3)^2 + (10-5)^2 ]^(1/2)
= [ 4^2 + 5^2 ]^(1/2)
= [41]^(1/2)

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

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21 Feb 2016, 21:26
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)

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

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22 Feb 2016, 00:01
1
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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22 Feb 2016, 15:01
1
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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23 Feb 2016, 01:41
1
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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Joined: 04 Jun 2016
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Re: In the coordinate plane, what is the distance between points (3, 5) an  [#permalink]

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14 Jul 2016, 07:05
1
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
$$d=\sqrt{(delta x)^2 +(delta y)^2}$$

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

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

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

$$d=\sqrt{41}$$

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

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06 Nov 2017, 08:43
1
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 = $$\sqrt{41}$$

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

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08 Nov 2017, 16:29
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

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Re: In the coordinate plane, what is the distance between points (3, 5) an &nbs [#permalink] 08 Nov 2017, 16:29
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