BREAKING: Target Test Prep releases Brand New 2026 On Demand GMAT prep course

Redeem
TTP OnDemand GMAT Video Course
Featured Course

Target Test Prep GMAT OnDemand

Scott Woodbury-Stewart’s private virtual classroom — 400 hours of master-class video lessons for the GMAT Focus Edition.

  • 715+ score guarantee — highest in the industry (99th percentile)
  • 52 chapters · 1,500+ lessons · 4,000+ practice questions
  • 400 hours of video · 1,500+ instructor-led HD smartboard lessons
  • 300,000+ students accepted to Harvard, Stanford, Wharton, Booth & Sloan & more
  • 24/7 live support + weekly Zoom office hours with GMAT instructors
  • TTP AI Assist — 24/7 AI-powered virtual tutor for instant help
  • 1,200+ flashcards + AI-powered study assistant & daily calendar
  • OnDemand, LiveTeach & GMAT Bootcamp formats available
  • Also: GRE, SAT Math & Executive Assessment courses
  • MBA Admissions Consulting now available
  • 🏆 2025 EdTech Breakthrough Award: Test Prep Solution Provider of the Year
  • 200,000+ students served
  • 5-day free trial — $0 to start, no auto-billing, cancel anytime
★★★★★ 5.0 (559 reviews)
130-pt guarantee
$0 to start then $127/mo
Start Free 5-Day Trial Read 559 Reviews →

Points A(1,4), B(2,2) and C(p,1) lie on the x-y coordinate p

Expert replies
Post new topic Post Reply
Previous Topic Next Topic
User avatar
Elite Legendary Member
Posts: 3991
Joined: Fri Jul 24, 2015 2:28 amFollowed by: 37 members
Location: Las Vegas, USA
Thanked: 19 times
by Max@Math Revolution » Wed Oct 03, 2018 11:50 pm

Timer

00:00

Answers

A

B

C

D

E

Stats

Difficulty—

[Math Revolution GMAT math practice question]

Points A(1,4), B(2,2) and C(p,1) lie on the x-y coordinate plane. If lines AB and BC are perpendicular to each other, p=?

A. -2
B. -1
C. 0
D. 1
E. 2
Top
Join the discussion
Log in to postLogin with Googleuse password
QUOTE IN REPLY
Source: — Problem Solving |
User avatar
GMAT Instructor
Posts: 1449
Joined: Sat Oct 09, 2010 2:16 pmFollowed by: 33 members
Thanked: 59 times

Points A(1,4), B(2,2) and C(p,1) lie on the x-y coordinate p

by fskilnik@GMATH » Thu Oct 04, 2018 5:58 am
Max@Math Revolution wrote:[Math Revolution GMAT math practice question]

Points A(1,4), B(2,2) and C(p,1) lie on the x-y coordinate plane. If lines AB and BC are perpendicular to each other, p=?

A. -2
B. -1
C. 0
D. 1
E. 2
$$?\,\, = \,p$$
Line AB is oblique (non-horizontal and non-vertical) therefore line BC is also oblique, and the product of their slopes must be -1.
$${\text{slope}}{\,_{\overleftrightarrow {{\text{AB}}}}}\,\, = \,\,\,\frac{{4 - 2}}{{1 - 2}}\,\, = \, - 2\,$$
$$\frac{1}{2}\,\,{\text{ = }}\,\,{\text{slope}}{\,_{\overleftrightarrow {{\text{BC}}}}}\,\,\,\,{\text{ = }}\,\,\frac{{2 - 1}}{{2 - p}}\,\,\,\,\,\,\,\, \Rightarrow \,\,\,\,\,\,p = 0$$

This solution follows the notations and rationale taught in the GMATH method.

Regards,
Fabio.
Fabio Skilnik :: GMATH method creator ( Math for the GMAT)
English-speakers :: https://www.gmath.net
Portuguese-speakers :: https://www.gmath.com.br
Top
Join the discussion
Log in to postLogin with Googleuse password
QUOTE IN REPLY
User avatar
Elite Legendary Member
Posts: 3991
Joined: Fri Jul 24, 2015 2:28 amFollowed by: 37 members
Location: Las Vegas, USA
Thanked: 19 times

by Max@Math Revolution » Sun Oct 07, 2018 5:22 pm
=>

The slope of the line segment joining the two points (x1,y1) and (x2,y2) is (y1-y2)/(x1-x2). The product of the slopes of perpendicular lines is -1.

The slope of the line AB is (4-2)/(1-2) = -2.
Since the two lines AB and BC are perpendicular each other, the slope of BC, which is (2-1)/(2-p), must be 1/2.
So,
(2-1)/(2-p)=1/2
1/(2-p)=1/2.
Thus, 2 - p = 2, and p = 0.

Therefore, the answer is C.
Answer: C
Top
Join the discussion
Log in to postLogin with Googleuse password
QUOTE IN REPLY
Post new topic Post Reply
• Page 1 of 1