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If points A, B, C lie in the xy plane, is the area of triangle ABC
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18 May 2018, 11:16
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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
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18 May 2018, 14:19
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. We get coordinates of B(3,4), but we don't know positions A and B  NS(2) All three points A, B, C lie in first quadrant only  clearly NS1+2) To satisfy condition 2 the extremes of A and B have to be located around X and Y axles in I quadrant , so A(0,4) and B(3,0). See attachment below. Answer (C)
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Re: If points A, B, C lie in the xy plane, is the area of triangle ABC
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18 May 2018, 19:02
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Looking at the uploaded picture, the triangle satisfies both statements and can be made infinitely large or infinitely small. Answer: E



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Re: If points A, B, C lie in the xy plane, is the area of triangle ABC
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14 Jul 2018, 23:32
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
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15 Jul 2018, 01:10
durgamadhab 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 Hi durgamadhab , 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 coordinates 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
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15 Jul 2018, 01:18
PKN wrote: durgamadhab 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 Hi durgamadhab , 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 coordinates 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. Answer is C 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
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15 Jul 2018, 01:26
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. Answer is C[/quote] 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
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15 Jul 2018, 01:57
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. Answer is C 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 xcoordinate on the line y=4 and to ycoordinate 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
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28 Jul 2018, 09:23
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
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28 Jul 2018, 09:23






