In the rectangular coordinate plane shown, what are the coordinates of

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)



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)

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

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

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.

Posted from my mobile device