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# Is the area of quadrilateral ABCD equal to area of quadrilateral AECD?

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28 Jul 2017, 01:20
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Is the area of quadrilateral ABCD equal to area of quadrilateral AECD?

(1) The coordinates of the points A, B, C and D are (0, 5), (6, 0), (0, −3) and (−2, 0), respectively.
(2) The point E lines on the line x = 6.
[Reveal] Spoiler: OA

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28 Jul 2017, 01:25
Bunuel wrote:
Is the area of quadrilateral ABCD equal to area of quadrilateral AECD?

(1) The coordinates of the points A, B, C and D are (0, 5), (6, 0), (0, −3) and (−2, 0), respectively.
(2) The point E lines on the line x = 6.

not sufficient

(2) Gives us x coordinate of point E
not sufficient

On combining

if E is same as B (6,0) then are is equal...otherwise not as the points A and C are not equidistant from B

Not Sufficient

E
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29 Jul 2017, 01:18
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mynamegoeson wrote:
Bunuel wrote:
Is the area of quadrilateral ABCD equal to area of quadrilateral AECD?

(1) The coordinates of the points A, B, C and D are (0, 5), (6, 0), (0, −3) and (−2, 0), respectively.
(2) The point E lines on the line x = 6.

not sufficient

(2) Gives us x coordinate of point E
not sufficient

On combining

if E is same as B (6,0) then are is equal...otherwise not as the points A and C are not equidistant from B

Not Sufficient

E

in your justification above, the statement B is not just giving us the X co-ordinate but also telling us the locus of that point.
if we follow that the base of triangle AEC will remain same as before(8 Units) and altitude will be (6 Units), constant distance of that line from Y Axis .
This will give us constant area irrespective of the location of point on the line.

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29 Jul 2017, 01:26
saurabhSuman wrote:
mynamegoeson wrote:
Bunuel wrote:
Is the area of quadrilateral ABCD equal to area of quadrilateral AECD?

(1) The coordinates of the points A, B, C and D are (0, 5), (6, 0), (0, −3) and (−2, 0), respectively.
(2) The point E lines on the line x = 6.

not sufficient

(2) Gives us x coordinate of point E
not sufficient

On combining

if E is same as B (6,0) then are is equal...otherwise not as the points A and C are not equidistant from B

Not Sufficient

E

in your justification above, the statement B is not just giving us the X co-ordinate but also telling us the locus of that point.
if we follow that the base of triangle AEC will remain same as before(8 Units) and altitude will be (6 Units), constant distance of that line from Y Axis .
This will give us constant area irrespective of the location of point on the line.

My approach to the problem will be same as given by mynamegoeson. For m it's difficult to understand how any co-ordinate of E will lead to the same area.

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29 Jul 2017, 01:51
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https://www.teachoo.com/4295/1052/Theor ... /Theorems/

also please try drawing the quadrilateral on co-ordinate axis if you have doubt wrt base begin same for all triangles

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15 Aug 2017, 15:41
isn't true that E can be anywhere on the line x=6? E can be at the same point as B, or it can be at any other point at x=6...

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15 Aug 2017, 18:55
saurabhSuman wrote:
https://www.teachoo.com/4295/1052/Theor ... /Theorems/

also please try drawing the quadrilateral on co-ordinate axis if you have doubt wrt base begin same for all triangles

Thanks Saurabh..

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15 Aug 2017, 20:14
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Expert's post
mvictor wrote:
isn't true that E can be anywhere on the line x=6? E can be at the same point as B, or it can be at any other point at x=6...

Hi...
The Quadrilateral consists of two triangles with Base as AC on y-axis.
1) first triangle ACD is Common, where base is AC and height is -2
2) second triangle ABC has base as AC and height is 6 and since statement II tells us that E is on x=6, it MEANS the height is 6 in ∆AED also..
So area will be same..

C
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17 Aug 2017, 21:15
When we get co-ordinate in the question .
It is always better to plot the co-ordinate and then solve the question . The task at hand is very easy then .

St1. only ABCD points are given . NO mention of E . Not sufficient
St2 . Only point E is given as ( 6,0) ==> x=6

together ,
the point B and E are same . Hence the ABCD = AECD
C ans .

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18 Aug 2017, 08:31
Stmt1 and Stmt2 alone are not sufficient.
On combining, We get 2 triangles for each quadrilateral
ABCD has ABC and ACD
AECD has AEC and ACD
Now, we have to see if area of ABC and AEC are same.
ABC and AEC has same base AC and same height 6 from AC to line x=6 so area will be same of both triangle.

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18 Aug 2017, 10:30
Just to clarify my thought to E.

Point E may lie on a line where x=6, but the Y coordinate could be different. Am I missing something?

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18 Aug 2017, 22:53
mcm2112 wrote:
Just to clarify my thought to E.

Point E may lie on a line where x=6, but the Y coordinate could be different. Am I missing something?

Yes, Y coordinate vary but area of triangle will remain the same as Area of triangle is $$\frac{1}{2}*BASE*HEIGHT$$
Base is common AC and Height is same distance from AC to x=6.

Hope I am clear.

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Is the area of quadrilateral ABCD equal to area of quadrilateral AECD?   [#permalink] 18 Aug 2017, 22:53
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