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28 Jun 2020, 12:40
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C
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
55%
(hard)
Question Stats:
71% (02:52) correct
29%
(02:37)
wrong
based on 247
sessions
History
Date
Time
Result
Not Attempted Yet
x=3
x=9
x=12−3y
\(y=\frac{−x}{3}+10\)
The lines created by the four equations above intersect at four points. What is the area of the quadrilateral created by those intersections?
A) 12
B) 21
C) 36
D) 49
E) 63
x=9
x=12−3y
\(y=\frac{−x}{3}+10\)
The lines created by the four equations above intersect at four points. What is the area of the quadrilateral created by those intersections?
A) 12
B) 21
C) 36
D) 49
E) 63
28 Jun 2020, 12:47
Kudos
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Attachment:
11.png [ 11.99 KiB | Viewed 7727 times ]
OFFICIAL EXPLANATION
As determined in the analysis of the question, the lines are two pairs of parallel lines, so their intersection forms a parallelogram. Determine the coordinates of the points by setting x to 3 and then to 9 in the third and fourth equations.
\(y=−\frac{1}{3}*(3)+4=3\)
\(y=−\frac{1}{3}*(3)+10=9\)
So the coordinates of the intersection of x = 3 with the other two lines are (3, 3) and (3, 9).
\(y=−\frac{1}{3}*(9)+4=1\)
\(y=−\frac{1}{3}*(9)+10=7\\
\)
The coordinates of the intersections with x = 9 are (9, 1) and (9, 7).
The area of a parallelogram is base × height. If you consider a side parallel to the y-axis the base, then the height is the distance between the two parallel lines, as shown by the dotted line on the sketch. So, the base is 7 − 1 = 6, and the height is 9 − 3 = 6. Therefore, the area of the parallelogram is 6 × 6 = 36, which is (C).
General Discussion
30 Jun 2020, 01:12
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coreyander
Lines (x=3 and x=9) are parallel to Y axis and are parallel
The horizontal distance between (x=3 and x=9) = 9-3. = 6 Units
Lines (x=12−3y and \(y=\frac{−x}{3}+10\)) hasve same slope i.e -1/3 so they are parallel)
Vertical Distance between (x=12−3y and \(y=\frac{−x}{3}+10\)) = Difference between their Y intercepts = 10-4 = 6
Given 4 lines make a parallelogram
Area of Parallelogram = Base * Height = 6*6 = 36
Answer: Option C
