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What is the distance between the points (–2, –2) and (4, 6)?

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Bunuel
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What is the distance between the points (–2, –2) and (4, 6)? [#permalink] New post   09 Oct 2018, 01:33
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What is the distance between the points (–2, –2) and (4, 6)?


(A) \(6\)

(B) \(7\)

(C) \(8\)

(D) \(10\)

(E) \(8\sqrt{2}\)
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D
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Abhishek009
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Re: What is the distance between the points (–2, –2) and (4, 6)? [#permalink] New post   09 Oct 2018, 08:33
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Bunuel wrote:
What is the distance between the points (–2, –2) and (4, 6)?


(A) \(6\)

(B) \(7\)

(C) \(8\)

(D) \(10\)

(E) \(8\sqrt{2}\)


\(Distance = \sqrt{(4 + 2)^2 + ( 6 + 2 )^2}\)

Or, \(Distance = \sqrt{36 + 64}\)

Or, \(Distance = \sqrt{100}\)

Or, Or, \(Distance = 10]\), Answer must be (D)
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BrentGMATPrepNow
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Re: What is the distance between the points (–2, –2) and (4, 6)? [#permalink] New post   09 Oct 2018, 11:44
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Bunuel wrote:
What is the distance between the points (–2, –2) and (4, 6)?


(A) \(6\)

(B) \(7\)

(C) \(8\)

(D) \(10\)

(E) \(8\sqrt{2}\)


I'd typically use the same approach that Abhishek009 used

However, another approach is to sketch the points and then create a right triangle as follows:


At this point, we can either use the Pythagorean Theorem to determine the length (of the hypotenuse), or recognize that we have an an enlarged version of the Pythagorean triplet 3-4-5
In our diagram, the length of the triangle's legs (6 and 8) are TWICE the measurements of 3 and 4.
So, the length of the third side must be TWICE the measurements of remaining side (5)

In either case, we find the length to be 10

Answer: D

Cheers,
Brent
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What is the distance between the points (–2, –2) and (4, 6)? [#permalink] New post   12 Oct 2019, 22:13
Bunuel wrote:
What is the distance between the points (–2, –2) and (4, 6)?


(A) \(6\)

(B) \(7\)

(C) \(8\)

(D) \(10\)

(E) \(8\sqrt{2}\)


The distance between any two points (x1,x2) and (y1,y2) on the coordinate plane can be computed using the formula \(\sqrt{(x2-x1)^2 + (y2-y1)^2}\)

In this question the coordinates are (–2, –2) and (4, 6). Plugging values into the formula we get:
\(\sqrt{(4-(-2))^2 + (6-(-2))^2}\)
\(\sqrt{(4+2)^2 + (6+2)^2}\)
\(\sqrt{(6)^2 + (8)^2}\)
\(\sqrt{36 + 64}\)= \(\sqrt{100}\) = \(10\)

Ans. D
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Re: What is the distance between the points (2, 2) and (4, 6)? [#permalink] New post   17 Nov 2022, 18:54
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Bunuel wrote:
What is the distance between the points (–2, –2) and (4, 6)?


(A) \(6\)

(B) \(7\)

(C) \(8\)

(D) \(10\)

(E) \(8\sqrt{2}\)


We can use the distance formula:

Distance = root[(4 - (-2))^2 + (6 - (-2))^2]

Distance = root[(4 + 2)^2 + (6 + 2)^2]

Distance = root[( 6)^2 + (8)^2]

Distance = root[36 + 64]

Distance = root(100) = 10

Answer: D
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Re: What is the distance between the points (2, 2) and (4, 6)? [#permalink]
17 Nov 2022, 18:54
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