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# The coordinates of points A and C are (0, -3) and (3, 3), respectively

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Math Expert
Joined: 02 Sep 2009
Posts: 60647
The coordinates of points A and C are (0, -3) and (3, 3), respectively  [#permalink]

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05 Dec 2019, 01:25
1
1
00:00

Difficulty:

65% (hard)

Question Stats:

67% (02:16) correct 33% (01:58) wrong based on 24 sessions

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The coordinates of points A and C are (0, -3) and (3, 3), respectively. If point B lies on line AC between points A and C, and if AB = 2BC, which of the following represents the coordinates of point B?

A. (1, -√5)
B. (1, -1)
C. (2, 1)
D. (1.5, 0)
E. (√5, √5)

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Joined: 16 Feb 2015
Posts: 264
Location: United States
Concentration: Finance, Operations
Re: The coordinates of points A and C are (0, -3) and (3, 3), respectively  [#permalink]

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05 Dec 2019, 03:01
1
1
Bunuel wrote:
The coordinates of points A and C are (0, -3) and (3, 3), respectively. If point B lies on line AC between points A and C, and if AB = 2BC, which of the following represents the coordinates of point B?

A. (1, -√5)
B. (1, -1)
C. (2, 1)
D. (1.5, 0)
E. (√5, √5)

Are You Up For the Challenge: 700 Level Questions

Explanantion: It’s a Section Formula problem (internal division case).

B (x’, y’) is such that

x’ = {mb+ na}/(m + n); y’ = {md + nc}/ (m + n).

In the given situation, a = 0, b = 3, c = -3, d = 3, m = 2 and n = 1.

we have x’ = (2 X 3 + 1 X 0)/3 = 2, and y’ = (2 X 3 + 1 X -3)/3 = 1,

the coordinates of point B are (2, 1).

IMO-C

Please Give Kudos, If you find my explanation Good Enough
Re: The coordinates of points A and C are (0, -3) and (3, 3), respectively   [#permalink] 05 Dec 2019, 03:01
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