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Using the given below solution, the problem can be solved much quicker.
But trigonometry (acc to my knowledge) is not in the scope of GMAT.
However, I have found that using basic trigonometry, a lot of GMAT problems can be solved much faster.

Anyway, the solution:

Since EC is perpendicular to the x axis, E,B and C will have the same x coordinate.
C's coorindates will be (6,0)
Let E's coorindates will be (6,y)

Attachment:
Screenshot 2019-04-02 at 15.59.35.png
Screenshot 2019-04-02 at 15.59.35.png [ 41.98 KiB | Viewed 6669 times ]

BC will be length 3
CD will be length 4
and AC will be length 6

Now, tan BAC = BC/AC = 3/6 = 1/2

also since BAC = CED

tan CED will also be equal to 1/2
tan CED=CD/CE=1/2
Hence 1/2=4/CE
CE= 8

Hence y = 8 and Coordinates of E are (6,8)
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Bunuel

In the rectangular coordinate plane shown, what are the coordinates of point E ?

(A) (2, 0)

(B) (2, 3)

(C) (6, 2)

(D) (6, 6)

(E) (6, 8)


Solution:

We see that the two triangles ABC and CDE are similar triangles, and the coordinates of C are (6, 0). So AC = 6 - 0 = 6 and CD = 6 - 2 = 4. Since BC = 3 - 0 = 3, and if we let CE = x, we can create the proportion (recall that the corresponding sides of similar triangles are proportional):

BC/AC = CD/CE

3/6 = 4/x

3x = 24

x = 8

Since CE = 8, the y-coordinate of E must be 0 + 8 = 8. Since C and E have the same x-coordinate, the coordinates of E are (6, 8).

Answer: E
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By the A-A Rule, the following Triangles are Similar:

Right Triangle ECD ~ Right Triangle ACB



Side Across from Angle a - Triangle ECD = 4 Units from Point D to Point C
___________________________________________________________

Side Across from Angle a - Triangle ACB = 3 Units, the Y-Coordinate of Point B



Let the Distance from Point B to Point E = Z



Side Across from UN-labeled Angle - Triangle ECD = 3 + Z, the Distance from Point C to Point E
______________________________________________________________________________

Side Across from UN-labeled Angle - Triangle ACB = 6, the Distance from Point A to Point C


4/3 = (3 + Z) / 6

Z = 5



the Distance on the Y-Axis from Point B to Point E must = 5 Units

The Y-Coordinate will thus be: (Point B's Y-Coordinate of 3) + 5 Units = +8

The X-Coordinate = 6


Answer - Point E is located at (6 , 8)

E
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scott Woodbury-Stewart
I am not understanding how ratios of corresponding sides are set.
Why BC/AC=CD/CE is correct? why BC/AC is not equal to CE/CD?
I am not clear with this very basic.

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