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

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Joined: 02 Sep 2009
Posts: 58458
What is the distance between the points (–2, –2) and (4, 6)?  [#permalink]

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09 Oct 2018, 01:33
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Difficulty:

5% (low)

Question Stats:

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

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

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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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09 Oct 2018, 11:44
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Top Contributor
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

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

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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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