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
Answer: A
Source: Veritas Prep
What is the area inscribed by the lines y =1, x = 1, y = 6-x on an xy-coordinate plane?
This topic has expert replies
-
- Legendary Member
- Posts: 1223
- Joined: Sat Feb 15, 2020 2:23 pm
- Followed by:1 members
Timer
00:00
Your Answer
A
B
C
D
E
Global Stats
GMAT/MBA Expert
- Brent@GMATPrepNow
- GMAT Instructor
- Posts: 16207
- Joined: Mon Dec 08, 2008 6:26 pm
- Location: Vancouver, BC
- Thanked: 5254 times
- Followed by:1268 members
- GMAT Score:770
First, let's graph the lines y = 1 and x = 1BTGModeratorVI wrote: ↑Sun Aug 02, 2020 7:00 amWhat 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
Answer: A
Source: Veritas Prep
![Image](https://i1168.photobucket.com/albums/r500/GMATPrepNow/a1_zps0ppp0p50.png)
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
![Image](https://i1168.photobucket.com/albums/r500/GMATPrepNow/a2_zpsrfgt0tio.png)
At this point, we can see that we have the following triangle.
![Image](https://i1168.photobucket.com/albums/r500/GMATPrepNow/a3_zpsedvhdjwu.png)
The base has length 4 and the height is 4
Area = (1/2)(base)(height)
= (1/2)(4)(4)
= 8
Answer: A