It is currently 23 Jan 2018, 14:05

Close

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
Your Progress

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

Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.

Close

Request Expert Reply

Confirm Cancel

Events & Promotions

Events & Promotions in June
Open Detailed Calendar

In ∆ ABC shown above, AB = BC and base AC is equal to the altitude of

  new topic post reply Question banks Downloads My Bookmarks Reviews Important topics  
Author Message
TAGS:

Hide Tags

Expert Post
Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 43380
In ∆ ABC shown above, AB = BC and base AC is equal to the altitude of [#permalink]

Show Tags

New post 15 Dec 2017, 01:05
00:00
A
B
C
D
E

Difficulty:

  35% (medium)

Question Stats:

67% (01:27) correct 33% (00:59) wrong based on 39 sessions

HideShow timer Statistics

Image
In ∆ ABC shown above, AB = BC and base AC is equal to the altitude of the triangle from point B. If the coordinates of points A and C are (2, 5) and (6, 5) respectively, which of the following could be the coordinates of point B?

(A) (2, 7)
(B) (2, 8)
(C) (2, 9)
(D) (4, 8)
(E) (4, 9)

[Reveal] Spoiler:
Attachment:
2017-12-15_1258_001.png
2017-12-15_1258_001.png [ 4.47 KiB | Viewed 427 times ]
[Reveal] Spoiler: OA

_________________

New to the Math Forum?
Please read this: Ultimate GMAT Quantitative Megathread | All You Need for Quant | PLEASE READ AND FOLLOW: 12 Rules for Posting!!!

Resources:
GMAT Math Book | Triangles | Polygons | Coordinate Geometry | Factorials | Circles | Number Theory | Remainders; 8. Overlapping Sets | PDF of Math Book; 10. Remainders | GMAT Prep Software Analysis | SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS) | Tricky questions from previous years.

Collection of Questions:
PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat

DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS; 9 Devil's Dozen!!!; 10 Number Properties set., 11 New DS set.


What are GMAT Club Tests?
Extra-hard Quant Tests with Brilliant Analytics

2 KUDOS received
Manager
Manager
avatar
S
Joined: 27 Oct 2017
Posts: 91
Location: India
Concentration: International Business, General Management
GPA: 3.64
WE: Business Development (Energy and Utilities)
In ∆ ABC shown above, AB = BC and base AC is equal to the altitude of [#permalink]

Show Tags

New post 15 Dec 2017, 07:23
2
This post received
KUDOS
Hi
The answer is E.
My explanation is as per attached sketch.
Please see how we can easily eliminate the choices A, B & C in a few seconds.

if you like the approach, appreciate by kudos. :thumbup:


Bunuel wrote:
Image
In ∆ ABC shown above, AB = BC and base AC is equal to the altitude of the triangle from point B. If the coordinates of points A and C are (2, 5) and (6, 5) respectively, which of the following could be the coordinates of point B?

(A) (2, 7)
(B) (2, 8)
(C) (2, 9)
(D) (4, 8)
(E) (4, 9)

[Reveal] Spoiler:
Attachment:
The attachment 2017-12-15_1258_001.png is no longer available

Attachments

WhatsApp Image 2017-12-15 at 20.54.16.jpeg
WhatsApp Image 2017-12-15 at 20.54.16.jpeg [ 102.63 KiB | Viewed 268 times ]


_________________

If you like my post, encourage me by providing Kudos...
Happy Learning...

VP
VP
avatar
P
Joined: 22 May 2016
Posts: 1260
Premium Member CAT Tests
In ∆ ABC shown above, AB = BC and base AC is equal to the altitude of [#permalink]

Show Tags

New post 15 Dec 2017, 09:03
Bunuel wrote:
Image
In ∆ ABC shown above, AB = BC and base AC is equal to the altitude of the triangle from point B. If the coordinates of points A and C are (2, 5) and (6, 5) respectively, which of the following could be the coordinates of point B?

(A) (2, 7)
(B) (2, 8)
(C) (2, 9)
(D) (4, 8)
(E) (4, 9)

[Reveal] Spoiler:
Attachment:
2017-12-15_1258_001.png

Four answers can be rejected quickly: A, B, C, and D.

The prompt makes it easy to find B's y-coordinate. We are given that the altitude from point B = base AC. Add the length of AC to 5 to find B's y-coordinate.

Length of AC: (6 - 2) = 4
Points A and C (and AC) are at y=5. Add the 4
(5 + 4) = 9 = B's y-coordinate

Eliminate answers A, B, and D, whose y-coordinates are not 9

Also eliminate Answer C (2, 9), for a number of reasons.* If B is at (2,9), directly above A, we now have a right isosceles triangle where AB = AC and hypotenuse BC does NOT equal AB. BC must = AC. Reject C.

Answer E is correct

AB = BC: ∆ ABC is isosceles. Its altitude is a perpendicular bisector of the base AC.

The altitude from B hits the base at AC's midpoint (4,5). The x-coordinate for AC's midpoint is (2+6)/2 = 4. The x-coordinate of B must be 4.

B is at (4,9)

Answer E

*If that doesn't stand out, think of side lengths and angle measures. AB = BC, so
∠A = ∠C (angles opposite equal sides are equal).

Imagine B "moving" to directly above A: ∠A gets bigger, ∠C gets smaller. Not possible; they're equal. Side AB gets shorter, side BC gets longer. Also not possible: AB = BC

_________________

At the still point, there the dance is. -- T.S. Eliot
Formerly genxer123

In ∆ ABC shown above, AB = BC and base AC is equal to the altitude of   [#permalink] 15 Dec 2017, 09:03
Display posts from previous: Sort by

In ∆ ABC shown above, AB = BC and base AC is equal to the altitude of

  new topic post reply Question banks Downloads My Bookmarks Reviews Important topics  


GMAT Club MBA Forum Home| About| Terms and Conditions| GMAT Club Rules| Contact| Sitemap

Powered by phpBB © phpBB Group | Emoji artwork provided by EmojiOne

Kindly note that the GMAT® test is a registered trademark of the Graduate Management Admission Council®, and this site has neither been reviewed nor endorsed by GMAC®.