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# What is the length of the line segment which connects points (a, b) an

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Math Expert
Joined: 02 Sep 2009
Posts: 58464
What is the length of the line segment which connects points (a, b) an  [#permalink]

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29 Aug 2018, 03:57
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Difficulty:

35% (medium)

Question Stats:

76% (01:21) correct 24% (01:35) wrong based on 46 sessions

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What is the length of the line segment which connects points (a, b) and (c, d)?

(1) Points (a, d) is 3 units from point (c, d).
(2) Points (a, d) is 4 units from point (a, b).

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Re: What is the length of the line segment which connects points (a, b) an  [#permalink]

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29 Aug 2018, 04:34
Bunuel wrote:
What is the length of the line segment which connects points (a, b) and (c, d)?

(1) Points (a, d) is 3 units from point (c, d).
(2) Points (a, d) is 4 units from point (a, b).

Combining
We know
* the distance from a to c from statement 1
*Distance from b to d from statement 2

Sufficient

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Re: What is the length of the line segment which connects points (a, b) an  [#permalink]

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29 Aug 2018, 05:12
Bunuel wrote:
What is the length of the line segment which connects points (a, b) and (c, d)?

(1) Points (a, d) is 3 units from point (c, d).
(2) Points (a, d) is 4 units from point (a, b).

(1) and (2) are individually insufficient.

But, with the combined data, you can see the points form a right angle triangle. And the Pythagoras theorem can be used to solve for the same.

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Re: What is the length of the line segment which connects points (a, b) an  [#permalink]

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29 Aug 2018, 14:16
2
Bunuel wrote:
What is the length of the line segment which connects points (a, b) and (c, d)?

(1) Points (a, d) is 3 units from point (c, d).
(2) Points (a, d) is 4 units from point (a, b).

Question stem:- What is the length of the line segment which connects points (a, b) and (c, d)?
$$Length=\sqrt{(c-a)^2+(d-b)^2}$$
we need the value of (c-a) and (d-b).

St1:- Points (a, d) is 3 units from point (c, d).
Observe that y-position of both the points are equal.
So distance between (a,d) and (c,d)=c-a=3-----------------(a)
No information on position of 'b' and 'd'.
Insufficient.

St2:- Points (a, d) is 4 units from point (a, b)
Observe that x-position of both the points are equal.
So distance between (a,d) and (a,b)=b-d=4 or d-b=-4-----------------(b)
No information on position of 'b' and 'd'.
Insufficient.

Combined, we have the value of c-a=3 and value of d-b=-4.
Sufficient.

Ans. (C)
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Re: What is the length of the line segment which connects points (a, b) an   [#permalink] 29 Aug 2018, 14:16
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