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If equation |x/2| + |y/2| = 5 encloses a certain region on the coordin

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Crytiocanalyst
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Re: If equation |x/2| + |y/2| = 5 encloses a certain region on the coordin [#permalink] New post  15 Jul 2021, 04:41
The key to solving the problem is finding the coordinates where the equation meets the axes with the extremems we can get the value of the figure
|x/2| + |Y/2| = 5
so when x = 0, y= |10|
when y=0 , x=|10|

we get the extrremums as (0,10),(10,0),(0,-10) and (-10,0).
it's a square whose one side has a value can be traced to as 10*2^1/2
area of the figure being 100*2 = 200
Hence IMO D
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rajshreeasati
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Re: If equation |x/2| + |y/2| = 5 encloses a certain region on the coordin [#permalink] New post  29 Apr 2022, 03:45
The best approach to such Coordinate Geometry Questions is always diagrams-
we have |x/2| + |y/2| = 5,
we will get 4 coordinates. x = 0, y = 10, y = 0, x = 10, x = 0, y = -10 and y = 0 and x = -10.
by drawing a diagram we get a figure where we have 4 triangles with 10 as the height and 10 as the base.
so area of region will be = 4 * 1/2 * 10*10 => 200.
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Noida
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If equation |x/2| + |y/2| = 5 encloses a certain region on the coordin [#permalink] New post  17 Nov 2022, 00:28
Equation of a line whose intercept on X-axis is (a,0) and Y-axis is (0,b) is
\(\frac{x}{a}+\frac{y}{b}=1\)

We get intercept points as (10,0) and (0,10).

Area of a triangle formed by these points and origin = \(\frac{(10*10)}{2}=50\)

Area of the region = 50*4 = 200
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If equation |x/2| + |y/2| = 5 encloses a certain region on the coordin [#permalink]
17 Nov 2022, 00:28
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