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# If points A, B, C lie in the xy plane, is the area of triangle ABC

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If points A, B, C lie in the xy plane, is the area of triangle ABC  [#permalink]

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18 May 2018, 10:16
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65% (hard)

Question Stats:

47% (01:33) correct 53% (01:41) wrong based on 96 sessions

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If points A, B, C lie in the xy plane, is the area of triangle ABC greater than 6 square units?

(1) Equation of line AB is y=4 and equation of line BC is x=3.

(2) All three points A, B, C lie in first quadrant only.
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If points A, B, C lie in the xy plane, is the area of triangle ABC  [#permalink]

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Updated on: 06 Sep 2018, 08:22

Originally posted by Hero8888 on 18 May 2018, 13:19.
Last edited by Hero8888 on 06 Sep 2018, 08:22, edited 2 times in total.
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Re: If points A, B, C lie in the xy plane, is the area of triangle ABC  [#permalink]

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18 May 2018, 18:02
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Attachment:

tri.png [ 16.7 KiB | Viewed 801 times ]

Looking at the uploaded picture, the triangle satisfies both statements and can be made infinitely large or infinitely small.

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Re: If points A, B, C lie in the xy plane, is the area of triangle ABC  [#permalink]

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14 Jul 2018, 22:32
amanvermagmat wrote:
If points A, B, C lie in the xy plane, is the area of triangle ABC greater than 6 square units?

(1) Equation of line AB is y=4 and equation of line BC is x=3.

(2) All three points A, B, C lie in first quadrant only.

Ans C: as axes do not come in any quadrant. As per both (1) and (2).... 0<x<=3 and 0<y<=4..... so area will be always less than 6 if the triangle lies in 1st quadrant
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Re: If points A, B, C lie in the xy plane, is the area of triangle ABC  [#permalink]

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15 Jul 2018, 00:10
amanvermagmat wrote:
If points A, B, C lie in the xy plane, is the area of triangle ABC greater than 6 square units?

(1) Equation of line AB is y=4 and equation of line BC is x=3.

(2) All three points A, B, C lie in first quadrant only.

Ans C: as axes do not come in any quadrant. As per both (1) and (2).... 0<x<=3 and 0<y<=4..... so area will be always less than 6 if the triangle lies in 1st quadrant

Your point is correct. However, the following are the points to ponder:-

1. In order to form a triangle , we have to consider the point of intersection of the lines AB & BC one of the vertices of triangle ABC. So, 'B' is the fixed vertices with co-ordinates B(3,4).

2. The points A & C have to lie necessarily on the line AB & BC respectively. (otherwise st1 is not validated)

3. ABC is a right angled triangle in the 1st quadrant.(As per st2)

4. With a fixed B; 0<AB<3 & 0<BC< infinity (subject to $$AC^2=AB^2+BC^2$$) (extending line BC vertically upward, C tends to have infinite no of positions))

5. Area of right angled triangle=$$\frac{1}{2}*AB*BC$$ can have more than one value of square units.

Hope this is sufficient to say our answer E.
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If points A, B, C lie in the xy plane, is the area of triangle ABC  [#permalink]

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15 Jul 2018, 00:18
PKN wrote:
amanvermagmat wrote:
If points A, B, C lie in the xy plane, is the area of triangle ABC greater than 6 square units?

(1) Equation of line AB is y=4 and equation of line BC is x=3.

(2) All three points A, B, C lie in first quadrant only.

Ans C: as axes do not come in any quadrant. As per both (1) and (2).... 0<x<=3 and 0<y<=4..... so area will be always less than 6 if the triangle lies in 1st quadrant

Your point is correct. However, the following are the points to ponder:-

1. In order to form a triangle , we have to consider the point of intersection of the lines AB & BC one of the vertices of triangle ABC. So, 'B' is the fixed vertices with co-ordinates B(3,4).

2. The points A & C have to lie necessarily on the line AB & BC respectively. (otherwise st1 is not validated)

3. ABC is a right angled triangle in the 1st quadrant.(As per st2)

4. With a fixed B; 0<AB<3 & 0<BC< infinity (subject to $$AC^2=AB^2+BC^2$$) (extending line BC vertically upward, C tends to have infinite no of positions))

5. Area of right angled triangle=$$\frac{1}{2}*AB*BC$$ can have more than one value of square units.

Hope this is sufficient to say our answer E.

When u take y=4, x=3 as two sides...and say the triangle will stay in first quadrant....the limits are fixed. maximum area of the triangle is certain.

another way....the area of the rectangle formed by lines y=4 and x=3 is.....3x4 = 12.
So the triangle will have a maximum area of 1/2 x area of rectangle...which is 1/2x12=6
But the points cannot be on the axes..... so the max area is 1/2 x 2.999999 x 3.999999= something less than 6
Ans C
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If points A, B, C lie in the xy plane, is the area of triangle ABC  [#permalink]

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15 Jul 2018, 00:26
When u take y=4, x=3 as two sides...and say the triangle will stay in first quadrant....the limits are fixed. maximum area of the triangle is certain.

y is NOT RESTRICTED ; it's range:- (0, INFINITY), which lie in 1st quadrant. So, we can't say what is the maximum area.

Given, y=4 is a line.
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If points A, B, C lie in the xy plane, is the area of triangle ABC  [#permalink]

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15 Jul 2018, 00:57
PKN wrote:
When u take y=4, x=3 as two sides...and say the triangle will stay in first quadrant....the limits are fixed. maximum area of the triangle is certain.

y is NOT RESTRICTED ; it's range:- (0, INFINITY), which lie in 1st quadrant. So, we can't say what is the maximum area.

Given, y=4 is a line.[/quote]

Answer is E..... but thats because there is no limit to the x-coordinate on the line y=4 and to y-coordinate of x=3. The triangle can be on any of the 4 sides of point of intersection (3,4)
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Re: If points A, B, C lie in the xy plane, is the area of triangle ABC  [#permalink]

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28 Jul 2018, 08:23
Can we get an expert's comments on this? I got the OA because with my reading of the question, I identified point b as (3,4), saw that ABC was a right triangle, and assumed that the triangle could be formed on any of the four sides of point (3,4) formed by lines y=4 and x=3. Looking at others' comments, I wonder if there is any reason why the triangle has to be inside of (3,4) as opposed to extending potentially infinitely outward?
Re: If points A, B, C lie in the xy plane, is the area of triangle ABC &nbs [#permalink] 28 Jul 2018, 08:23
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