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16 Sep 2014, 01:29
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If the graph of the equation \(|\frac{x}{3}|+|\frac{y}{9}|=10\) encloses a certain region on the coordinate plane, what is the area of that region?
A. \(675\)
B. \(1350\)
C. \(2700\)
D. \(5400\)
E. \(10800\)
A. \(675\)
B. \(1350\)
C. \(2700\)
D. \(5400\)
E. \(10800\)
16 Sep 2014, 01:29
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Bookmarks
Official Solution:
If the graph of the equation \(|\frac{x}{3}|+|\frac{y}{9}|=10\) encloses a certain region on the coordinate plane, what is the area of that region?
A. \(675\)
B. \(1350\)
C. \(2700\)
D. \(5400\)
E. \(10800\)
Let's find the \(x\) and \(y\) intercepts.
When \(y = 0\), we have \(x = 30\) or \(x = -30\).
When \(x = 0\), we have \(y = 90\) or \(y = -90\).
So, we have 4 points: (30, 0), (-30, 0), (0, 90), and (0, -90). When connecting these points, we obtain the following rhombus:
The area of a rhombus can be calculated as \(\frac{d_1 * d_2}{2}\), where \(d_1\) and \(d_2\) are the lengths of the diagonals. Thus, the area of the enclosed figure is \(\frac{60 * 180}{2} = 5,400\).
Answer: D
If the graph of the equation \(|\frac{x}{3}|+|\frac{y}{9}|=10\) encloses a certain region on the coordinate plane, what is the area of that region?
A. \(675\)
B. \(1350\)
C. \(2700\)
D. \(5400\)
E. \(10800\)
Let's find the \(x\) and \(y\) intercepts.
When \(y = 0\), we have \(x = 30\) or \(x = -30\).
When \(x = 0\), we have \(y = 90\) or \(y = -90\).
So, we have 4 points: (30, 0), (-30, 0), (0, 90), and (0, -90). When connecting these points, we obtain the following rhombus:
The area of a rhombus can be calculated as \(\frac{d_1 * d_2}{2}\), where \(d_1\) and \(d_2\) are the lengths of the diagonals. Thus, the area of the enclosed figure is \(\frac{60 * 180}{2} = 5,400\).
Answer: D
01 Nov 2018, 09:49
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In case you don't have the equation for the area of a rhombus memorized, you could have also multiplied the area of a triangle by 4. This figure is made up of 4 equal triangles.
Area of triangle = 1/2bh
Area of our figure=4*(1/2*30*90)=5400
Answer=D.
Area of triangle = 1/2bh
Area of our figure=4*(1/2*30*90)=5400
Answer=D.
