Carcass wrote:
Attachment:
#GREpracticequestion In the rectangular.png
In the rectangular coordinate system, segment OP is rotated counterclockwise through an angle of 90° to position OQ (not shown).
Quantity A |
Quantity B |
The x-coordinate of point \(Q\) |
\(-1\) |
The two given coordinates (√3, 1) should remind us of the
special 30-60-90 right triangle.
If we draw a line from the point that is perpendicular to the x-axis, we get a right triangle.
This means we can apply the Pythagorean theorem to determine that the length of the line segment is 2.
At this point, we can see the special 30-60-90 right triangle hiding in the diagram.
When we rotate the line segment 90 degrees, the length of the line segment is still 2.
If we draw a line from the new point to the x-axis, we get another a right triangle.
More importantly, we can see that our new right triangle is also a 30-60-90 right triangle, which means it has the following lengths.
From here we can see that (-1, √3) are the coordinates of the new point.
The x-coordinate of the new point is -1, which means Quantities A and B are equal.
Answer: C
Cheers,
Brent
Sir, a great explanation in the first place! But, still I'm not able to understand completely. When rotated 90 degrees, how did the corresponding angles 30 and 60 interchange? Can you explain the thought process behind this?