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

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What is the distance between the points (–2, –2) and (4, 6)?  [#permalink]

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New post 09 Oct 2018, 01:33
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A
B
C
D
E

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  5% (low)

Question Stats:

90% (00:48) correct 10% (01:58) wrong based on 48 sessions

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Re: What is the distance between the points (–2, –2) and (4, 6)?  [#permalink]

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New post 09 Oct 2018, 08:33
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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Re: What is the distance between the points (–2, –2) and (4, 6)?  [#permalink]

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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:
Image

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]

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