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.

Thank you for using the timer!
We noticed you are actually not timing your practice. Click the START button first next time you use the timer.
There are many benefits to timing your practice, including:

Mark your calendars - All GMAT Club Tests are free and open November 22nd to celebrate Thanksgiving Day! Access will be available from 0:01 AM to 11:59 PM, Pacific Time (USA)

We are supposed to find the area of the figure enclosed by the lines x=1, y=1 and y=6-x which is nothing but Area of Triangle ABC. AB = 4 (distance between (1,1) and (5,1)) AC = 4 (distance between (1,1) and (1,5))

Area of Triangle ABC which is right angled at A = (1/2) * AB * AC = (1/2)*4*4 = 8 So, Answer A

Hope it helps!

PawanRamnani1234 wrote:

What is the area inscribed by the lines y =1, x = 1, y = 6-x on an xy-coordinate plane?

a) 8 b) 10 c) 12 d) 14 e) 18

Looking for appropriate solution for above problem.

Re: What is the area inscribed by the lines y =1, x = 1, y = 6-x on an xy-
[#permalink]

Show Tags

08 Sep 2016, 07:04

1

Top Contributor

PawanRamnani1234 wrote:

What is the area inscribed by the lines y =1, x = 1, y = 6-x on an xy-coordinate plane?

a) 8 b) 10 c) 12 d) 14 e) 18

First, let's graph the lines y = 1 and x = 1

At this point, we need to find the points where the line y = 6-x INTERSECTS the other two lines.

For the vertical line, we know that x = 1, so we'll PLUG x = 1 into the equation y = 6-x to get y = 6-1 = 5 Perfect, when x = 1, y = 5, so one point of intersection is (1,5)

For the horizontal line, we know that y = 1, so we'll PLUG y = 1 into the equation y = 6-x to get 1 = 6-x. Solve to get: x = 5 So, when y = 1, x = 5, so one point of intersection is (5,1)

Now add these points to our graph and sketch the line y = 5-x

At this point, we can see that we have the following triangle.

The base has length 4 and the height is 4 Area = (1/2)(base)(height) = (1/2)(4)(4) = 8

Re: What is the area inscribed by the lines y =1, x = 1, y = 6-x on an xy-
[#permalink]

Show Tags

08 Sep 2016, 08:23

PawanRamnani1234 wrote:

What is the area inscribed by the lines y =1, x = 1, y = 6-x on an xy-coordinate plane?

a) 8 b) 10 c) 12 d) 14 e) 18

Hi,

The sketches have been made above, but few points.. 1) Three equation,so three lines and therefore a triangle..two sides x=1and y=1 make a right angle so we are talking of a RIGHT angle triangle.. 2) the third line will intersect these two lines .. On line x=1, when x is 1 in y=6-x, y=6-1=5.. similarly on line y=1at x=5.. 3) therefore the length of each side is 5-1=4.. Area =1/2*4*4=8.. A
_________________

Re: What is the area inscribed by the lines y =1, x = 1, y = 6-x on an xy-
[#permalink]

Show Tags

16 Jun 2017, 00:02

PawanRamnani1234 wrote:

What is the area inscribed by the lines y =1, x = 1, y = 6-x on an xy-coordinate plane?

a) 8 b) 10 c) 12 d) 14 e) 18

There's no need to actually diagram this problem- simply not much time on the GMAT; however, it might be ok in the beginning. Anyways, the concept behind this question is simply testing your ability to plug in the given y and x values in order to find the two other vertices of the figure- which if you do diagram you'll see is an isosceles equilateral triangle.

1= 6-x -5=-x 5=x (we're not done yet though)

y=6-(x) y=6- 1 y= 5 ( we are done yet either)

x and y intersect at (1,1) so actually each length of this triangle would be 4= 4 spots upwards from (1,1) actually gives us (1,5) - the vertice of the triangle derived from plugging in our x value; And 4 spots to the right of (1,1) gives us (5,1) the vertice of the triangle derived from plugging in the y value. And because this triangle is a right triangle (the intersection of two perfectly straight lines, lines with a slope of 0, is 90 degrees and the lines x and y are also perpendicular) the area can be calculated simply by

Re: What is the area inscribed by the lines y =1, x = 1, y = 6-x on an xy-
[#permalink]

Show Tags

21 Sep 2018, 21:49

Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email.
_________________