Re: In the rectangular coordinate plane shown, what are the coo
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22 Feb 2020, 13:23
The official explanation
From the figure, since EC is perpendicular to the x-axis, C is a point vertically below point B. Hence, both have the same x-coordinate.
The line AC is horizontal and therefore its length equals the x-coordinate difference of A and C, which equals 6 – 0 = 6.
The line DC is horizontal and therefore its length equals the x-coordinate difference of D and C, which is 6 – 2 = 4.
The length of the vertical line BC equals the y-coordinate difference of B and C, which is 3 – 0 = 3.
The length of the vertical line EC equals the y-coordinate difference of E and C.
Now, in ∆ABC, ∠A = a°, ∠B = 90° – a°, and ∠C = 90°. The sides opposite angles A and B are in the ratio BC/AC = 3/6 = 1/2.
Similarly, in ∆DEC, ∠E = a°, ∠D = 90° – a°, and ∠C = 90° (So, ABC and DEC are similar triangles and their corresponding sides are proportional).
Hence, the sides opposite angles E and D are in the ratio DC/EC = 1/2. Hence, we have DC/EC = 1/2 EC = 2DC EC = 2 ⋅ 4 = 8
Hence, the y-coordinate of point E is 8, and the answer is (E).