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

Question

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.

BrentGMATPrepNow · Accepted Answer

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

Skywalker18 · Answer

Distance between (3, 5) and (7, 10)
=  ^(1/2)
=  ^(1/2)
=  ^(1/2)

Answer E

rajatmahan · Answer

Distance between 2 points is  ^1/2

=  ^(1/2)
=  ^(1/2)
=  ^(1/2)

Thus answer is E

nipunjain14 · Answer

sqrt((y2-y1)^2 +(x2-x1)^2)
thus 
sqrt((10-5)^2+(7-3)^2)
sqrt(25+16)= sqrt(41)

Ans:
E

TeamGMATIFY · Answer

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

LogicGuru1 · Answer

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

generis · Answer

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

JeffTargetTestPrep · Answer

We can use the distance formula:

d = √

d = √(5^2 + 4^2)

d = √(25 + 16) = √41

Answer: E

ConfusedSEA · Answer

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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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

Prep Toolkit

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