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If the area of right triangle ABC is 30, what are the coordinates of
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12 Oct 2015, 20:55
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Re: If the area of right triangle ABC is 30, what are the coordinates of
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12 Oct 2015, 22:33
Bunuel wrote: If the area of right triangle ABC is 30, what are the coordinates of point B ? A. (9, 4) B. (4, 9) C. (3, 4) D. (3, 9) E. (12, 4) Attachment: Geometry_Q9Image.pg.jpg Kudos for a correct solution.Point B will have same Y coordinate as Point A has i.e. 4. Hence, Option A, C and E remaining and other two options B and D are ruled out Area of Triangle ABC = (1/2)*AB*AC = 30 (Given) But AC = 5 (Distance of Y coordinate from 1 to 4 as X coordinates of A and C are same) i.e. Area of Triangle ABC = (1/2)*AB*5 = 30 i.e. AB = 12 Horizontal Distance of 12 from X coordinate of point A (3) = 3+12 = +9 i.e. Coordinate of point B = (9, 4) Answer: Option A
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Re: If the area of right triangle ABC is 30, what are the coordinates of
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13 Oct 2015, 03:11
Triangle ABC is right triangle. So the area of ABC will be equal to half the product of its legs. Also, length of leg AC is (4 (1)) = 4 + 1 = 5 (We can do this because xcoordinate is the same) => 30 = 1/2 * AC * AB = 1/2 * 5 * AB =>AB = 60/5 = 12.
We know that ABC is a right angled triangle. And one of its legs if parallel to yaxis. So, the other leg must be parallel to xaxis and the ycoordinate of points A and B must be same. xcoordinate of leg AB = 3 + 12 = 9 So, coordinates of point B are (x,y) = (9,4)
Ans. A



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Re: If the area of right triangle ABC is 30, what are the coordinates of
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13 Oct 2015, 06:59
Segment AC has a length of 4(1)=5.
Given that ABC is a right triangle, (AB*AC)/2=30. Therefore AB*5=60, AB=12.
Since the X coordinate of A and C are the same, you know that the Y coordinate of A and B would be the same as well.
To get the length of AB, just take 3+12=9. Point B is located at point (9,4). The answer is A



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Re: If the area of right triangle ABC is 30, what are the coordinates of
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18 Oct 2015, 11:30
Bunuel wrote: If the area of right triangle ABC is 30, what are the coordinates of point B ? A. (9, 4) B. (4, 9) C. (3, 4) D. (3, 9) E. (12, 4) Attachment: Geometry_Q9Image.pg.jpg Kudos for a correct solution. VERITAS PREP OFFICIAL SOLUTION:Since side (AC) is parallel to the yaxis (based on the fact that they have the same xcoordinate) and we know that angle BAC is a right angle, we can conclude that side (AB) is parallel to the xaxis and therefore, once we determine the length, it’s simply a matter of moving that distance horizontally to the right. To determine the length of that side, use the formula for the area of a triangle: 1/2*(base)(height) = area. We know the area is 30 from given information, and can calculate that (AC) has a length of 5. Using h for the unknown, we can calculate 1/2(5)(h) = 30 and solve that h= 12. Since (AB) has a length of 12, simply add 12 to the xcoordinate for the coordinates of point B, (9, 4).
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Re: If the area of right triangle ABC is 30, what are the coordinates of
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18 Oct 2015, 11:43
Logically, we can get to the right answer without any calculations:
A. (9, 4)
y interceptor of point B must be 4, therefore, we can eliminate B. (4, 9) and D. (3, 9). We know that AC = 5, which means that AB must be equal to 12. We can eliminate C because it tells us the xinterceptor of point B is 3, and E because it tells us that xinterceptor of point B is 12, which is as well impossible. The only correct answer choice left is A.



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Re: If the area of right triangle ABC is 30, what are the coordinates of
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15 Jun 2017, 20:39
Bunuel wrote: If the area of right triangle ABC is 30, what are the coordinates of point B ? A. (9, 4) B. (4, 9) C. (3, 4) D. (3, 9) E. (12, 4) Attachment: Geometry_Q9Image.pg.jpg Kudos for a correct solution.Quite Simply, we are given the area of the triangle, a right triangle, so we can just use algebra to solve for the base. We know that one side of the triangle is 5 as indicated by the difference in y coordinates 1 and 4 so using the formula for the area of the right triangle we can reverse engineer 5 x Base / 2 = 30 5 *Base = 60 Base = 12 On that same logic, because we know the x coordinate of a point directly across from point B ( has the same y value) we can just find the difference by taking the absolute value of the x coordinate and using algebra to solve 3 + x= 12 x= 9 More fundamentally, if you count 3 spots to the right from the vertice of the triangle (3 , 4) you will be at (0,4) and if you move three spots to the right you would be at (9,4) which would give you a total length of twelve for the base. Thus A



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Re: If the area of right triangle ABC is 30, what are the coordinates of
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30 Aug 2018, 01:55
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