• 1 Hour Free
BEAT THE GMAT EXCLUSIVE

Available with Beat the GMAT members only code

• Most awarded test prep in the world
Now free for 30 days

Available with Beat the GMAT members only code

• Magoosh
Study with Magoosh GMAT prep

Available with Beat the GMAT members only code

• Free Veritas GMAT Class
Experience Lesson 1 Live Free

Available with Beat the GMAT members only code

• Award-winning private GMAT tutoring
Register now and save up to \$200

Available with Beat the GMAT members only code

• Free Trial & Practice Exam
BEAT THE GMAT EXCLUSIVE

Available with Beat the GMAT members only code

• Free Practice Test & Review
How would you score if you took the GMAT

Available with Beat the GMAT members only code

• Get 300+ Practice Questions

Available with Beat the GMAT members only code

• 5-Day Free Trial
5-day free, full-access trial TTP Quant

Available with Beat the GMAT members only code

• 5 Day FREE Trial
Study Smarter, Not Harder

Available with Beat the GMAT members only code

## In the rectangular coordinate (OG16)

This topic has 3 expert replies and 0 member replies
boomgoesthegmat Senior | Next Rank: 100 Posts
Joined
25 Apr 2016
Posted:
93 messages
1

#### In the rectangular coordinate (OG16)

Thu May 19, 2016 3:48 pm

In the rectangular coordinate system above, if point R (not shown) lies on the positive y-axis and the area of triangle ORP is 12, what is the y-coordinate of point R?

A) 3
B) 6
C) 9
D) 12
E) 24

OA: B

### GMAT/MBA Expert

EconomistGMATTutor GMAT Instructor
Joined
04 Oct 2017
Posted:
545 messages
Followed by:
10 members
180
Wed Dec 13, 2017 6:39 am
Quote:
In the rectangular coordinate system above, if point R (not shown) lies on the positive y-axis and the area of triangle ORP is 12, what is the y-coordinate of point R?

A) 3
B) 6
C) 9
D) 12
E) 24
Hi boomgoesthegmat,
Let's take a look at your question.

The coordinates of P are (4, 0), therefore,
$$OP=4$$
Area of triangle ORP = 12

We know that:
Area of a triangle = (1/2) * (Base) * (Height)
$$Area=\frac{1}{2}\cdot OQ\cdot OP$$
$$12=\frac{1}{2}\cdot OQ\cdot4$$
$$12=OQ\cdot2$$
$$OQ=\frac{12}{2}$$
$$OQ=6$$

So the y-coordinate of Q is 6.
Therefore, Option B is correct.

Hope it helps.
I am available if you'd like any follow up.

_________________
GMAT Prep From The Economist
We offer 70+ point score improvement money back guarantee.
Our average student improves 98 points.

Free 7-Day Test Prep with Economist GMAT Tutor - Receive free access to the top-rated GMAT prep course including a 1-on-1 strategy session, 2 full-length tests, and 5 ask-a-tutor messages. Get started now.

### GMAT/MBA Expert

Scott@TargetTestPrep GMAT Instructor
Joined
25 Apr 2015
Posted:
792 messages
Followed by:
3 members
43
Tue Dec 12, 2017 6:32 am
boomgoesthegmat wrote:

In the rectangular coordinate system above, if point R (not shown) lies on the positive y-axis and the area of triangle ORP is 12, what is the y-coordinate of point R?

A) 3
B) 6
C) 9
D) 12
E) 24
'
We are given that point P lies at (4,0) and point R lies on the y-axis. Thus, we see that we have a right triangle with one vertex at point P, another at coordinate (0,0), and the other at point R. Thus, the base of the triangle is 4, and the height is the y-coordinate of point R.

Since we know the area of the triangle is 12, we can create the following equation in which y = the y-coordinate of point R.

area = (base x height)/2

12 = 4y/2

24 = 4y

6 = y

_________________
Scott Woodbury-Stewart Founder and CEO

### GMAT/MBA Expert

Rich.C@EMPOWERgmat.com Elite Legendary Member
Joined
23 Jun 2013
Posted:
9207 messages
Followed by:
473 members
2867
GMAT Score:
800
Thu May 19, 2016 4:53 pm
Hi boomgoesthegmat,

From the diagram, we know that the base of triangle ORP = 4. We also know that it's area = 12, so we can combine those two pieces of information to find the height of the triangle (and by extension, the Y co-ordinate of point R).

Area = (1/2)(base)(height)

12 = (1/2)(4)(height)
12 = 2(height)
6 = height

GMAT assassins aren't born, they're made,
Rich

_________________
Contact Rich at Rich.C@empowergmat.com

### Best Conversation Starters

1 lheiannie07 108 topics
2 Roland2rule 63 topics
3 ardz24 63 topics
4 LUANDATO 52 topics
5 Vincen 50 topics
See More Top Beat The GMAT Members...

### Most Active Experts

1 GMATGuruNY

The Princeton Review Teacher

144 posts
2 Jeff@TargetTestPrep

Target Test Prep

115 posts
3 Rich.C@EMPOWERgma...

EMPOWERgmat

111 posts
4 Scott@TargetTestPrep

Target Test Prep

101 posts
5 Max@Math Revolution

Math Revolution

87 posts
See More Top Beat The GMAT Experts