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# In the rectangular coordinate system above, if point (a, b), shown, an

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Joined: 02 Sep 2009
Posts: 55150
In the rectangular coordinate system above, if point (a, b), shown, an  [#permalink]

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05 Jul 2018, 21:36
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15% (low)

Question Stats:

81% (01:52) correct 19% (02:04) wrong based on 73 sessions

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In the rectangular coordinate system above, if point (a, b), shown, and the two points (4a, b) and (2a, 2b), not shown, were connected by straight lines, then the area of the resulting triangular region, in terms of a and b, would be

(A) ab/2

(B) ab

(C) 3ab/2

(D) 2ab

(E) 4ab

Attachment:

20160425060058164.jpg [ 11.99 KiB | Viewed 1036 times ]

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In the rectangular coordinate system above, if point (a, b), shown, an  [#permalink]

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Updated on: 05 Jul 2018, 22:01
3
Hi,

Solve the determinant
1/2*
| x1 y1 1|
| x2 y2 1|
| x3 y3 1|
to get the area of the triangle. The answer comes out to be C

If you are not comfortable solving determinants, please use Area of triangle = 1/2∗|(x1y2−y1x2)+(x2y3−y2x3)+(x3y1−y3x1)|

Originally posted by munzuto on 05 Jul 2018, 21:56.
Last edited by munzuto on 05 Jul 2018, 22:01, edited 1 time in total.
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Re: In the rectangular coordinate system above, if point (a, b), shown, an  [#permalink]

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05 Jul 2018, 21:58
2
Bunuel wrote:

In the rectangular coordinate system above, if point (a, b), shown, and the two points (4a, b) and (2a, 2b), not shown, were connected by straight lines, then the area of the resulting triangular region, in terms of a and b, would be

(A) ab/2

(B) ab

(C) 3ab/2

(D) 2ab

(E) 4ab
Attachment:
20160425060058164.jpg

Given triangle with co-ordinates (a, b),(4a, b) and (2a, 2b).

length of base=4a-a=3a unit
length of height=2b-b=b unit

Area of triangle=$$\frac{1}{2}*base*height$$=$$\frac{1}{2}*3a*b$$=$$\frac{3ab}{2}$$

Ans. (C)
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In the rectangular coordinate system above, if point (a, b), shown, an  [#permalink]

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09 Jul 2018, 15:52
These kinds of questions should be visualizedin order to make them easier for the further analysis. In more detail, one can imagine the points (a,b) as (1,1). Afterward, it will be more visually appropriate to imagine the points (4a,b) and (2a,2b). When one draws them in the coordinate system, the triangle becomes apparent. Thus one can see both the height and the base more easily, and make further judgments. In this case, the 3a turns out to be the height(or base) and the b to the base. So the afterward calculation I am sure that everybody knows.
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Re: In the rectangular coordinate system above, if point (a, b), shown, an  [#permalink]

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04 Mar 2019, 12:07
A = 2
B = 2

Get the point 2,2
Then 4(2), 1
Finally 2(2), 2(2)

Get the three points: 2,2; 8,2; 4,4; -> to the height of 8-2 = 6 & base of 4 - 2 = 2

A = B*H *1/2 -> 6*2 *(1/2) = 6

Plug into the answer choices and C derives 6
3(2)(2) / 2 = 6
Re: In the rectangular coordinate system above, if point (a, b), shown, an   [#permalink] 04 Mar 2019, 12:07
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