It is currently 17 Feb 2019, 00:32

### GMAT Club Daily Prep

#### Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.

Customized
for You

we will pick new questions that match your level based on your Timer History

Track

every week, we’ll send you an estimated GMAT score based on your performance

Practice
Pays

we will pick new questions that match your level based on your Timer History

# The points A( 0, 0), B( 0, 4a – 5), and C( 2a + 1, 2a + 6) f

Author Message
TAGS:
Moderator
Joined: 18 Apr 2015
Posts: 5532
Followers: 89

Kudos [?]: 1113 [0], given: 5130

The points A( 0, 0), B( 0, 4a – 5), and C( 2a + 1, 2a + 6) f [#permalink]  30 Nov 2018, 18:11
Expert's post
00:00

Question Stats:

75% (03:13) correct 25% (03:30) wrong based on 4 sessions
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
[Reveal] Spoiler: OA

_________________
Intern
Joined: 05 Dec 2018
Posts: 9
Followers: 0

Kudos [?]: 0 [0], given: 0

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 Y-Coordinates of B & C should be same as they are on the same line i.e BC.
4a-5 = 2a+6
a=11/2
So
A= (0,0)
B=(0,4a-5)=(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.
Supreme Moderator
Joined: 01 Nov 2017
Posts: 349
Followers: 4

Kudos [?]: 98 [0], given: 2

Re: The points A( 0, 0), B( 0, 4a – 5), and C( 2a + 1, 2a + 6) f [#permalink]  06 Dec 2018, 18:32
Expert's post
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 y-axis, and 90° is at B, the y-coordinates of B and C should be the same.
So $$4a-5=2a+6.......2a=11.....a=\frac{11}{2}$$..
Now AB is nothing but y-coordinates of B and BC is nothing but x-coordinates 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
_________________

Some useful Theory.
1. Arithmetic and Geometric progressions : https://greprepclub.com/forum/progressions-arithmetic-geometric-and-harmonic-11574.html#p27048
2. Effect of Arithmetic Operations on fraction : https://greprepclub.com/forum/effects-of-arithmetic-operations-on-fractions-11573.html?sid=d570445335a783891cd4d48a17db9825
3. Remainders : https://greprepclub.com/forum/remainders-what-you-should-know-11524.html
4. Number properties : https://greprepclub.com/forum/number-property-all-you-require-11518.html
5. Absolute Modulus and Inequalities : https://greprepclub.com/forum/absolute-modulus-a-better-understanding-11281.html

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