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The points A( 0, 0), B( 0, 4a – 5), and C( 2a + 1, 2a + 6) f [#permalink]
30 Nov 2018, 18:11
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The points A( 0, 0), B( 0, 4a – 5), and C( 2a + 1, 2a + 6) form a triangle. If ∠ ABC = 90 °, what is the area of triangle ABC? A. 102 B. 120 C. 132 D. 144 E. 156
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Re: The points A( 0, 0), B( 0, 4a – 5), and C( 2a + 1, 2a + 6) f [#permalink]
06 Dec 2018, 01:37
As angle ABC is 90. This is a right triangle with base AB and height BC. So area of Triangle is 1/2 (AB). BC BC is perpendicular to AB. And A is at origin (0,0). The YCoordinates of B & C should be same as they are on the same line i.e BC. 4a5 = 2a+6 a=11/2 So A= (0,0) B=(0,4a5)=(0,17) C=(2a+1,2a+6)=(12,17) Find distances AB & BC AB = 17 BC = 12 Area of triangle = 1/2 (17)(12) = 102 It's A.



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Re: The points A( 0, 0), B( 0, 4a – 5), and C( 2a + 1, 2a + 6) f [#permalink]
06 Dec 2018, 18:32
Carcass wrote: The points A( 0, 0), B( 0, 4a – 5), and C( 2a + 1, 2a + 6) form a triangle. If ∠ ABC = 90 °, what is the area of triangle ABC?
A. 102
B. 120
C. 132
D. 144
E. 156 90° is at B so area will be (AB*BC)/2 Since coordinates of x in A and B are the same that is 0, meaning A and B lie on yaxis, and 90° is at B, the ycoordinates of B and C should be the same. So \(4a5=2a+6.......2a=11.....a=\frac{11}{2}\).. Now AB is nothing but ycoordinates of B and BC is nothing but xcoordinates of C 1)So X coordinates of C are \(2a+1=2*\frac{11}{2}+1=11+1=12\) 2) y coordinates of B = \(2a+6=2*\frac{11}{2}+6=11+6=17\) Area = \(\frac{12*17}{2}=6*17=102\) A
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Some useful Theory. 1. Arithmetic and Geometric progressions : https://greprepclub.com/forum/progressionsarithmeticgeometricandharmonic11574.html#p27048 2. Effect of Arithmetic Operations on fraction : https://greprepclub.com/forum/effectsofarithmeticoperationsonfractions11573.html?sid=d570445335a783891cd4d48a17db9825 3. Remainders : https://greprepclub.com/forum/remainderswhatyoushouldknow11524.html 4. Number properties : https://greprepclub.com/forum/numberpropertyallyourequire11518.html 5. Absolute Modulus and Inequalities : https://greprepclub.com/forum/absolutemodulusabetterunderstanding11281.html




Re: The points A( 0, 0), B( 0, 4a – 5), and C( 2a + 1, 2a + 6) f
[#permalink]
06 Dec 2018, 18:32





