The point (-3, 2) is rotated 90° clockwise around the origin to point
[#permalink]
24 Mar 2021, 19:30
Reflection 1:
The way I understood 90 degree rotations was by the “tipping the rectangle” method.
It sounds goofy, but:
Start with Original Point (-3, 2)
Since we are rotating 90 degrees about the Origin (0 , 0) ——> make a rectangle with these 2 points
Label (-3 , 2) as point A and Origin as Point O
If we join the horizontal and vertical lines to the Y and X axis, respectively, we end up with a rectangle that is 3 units along the Negative X Axis and 2 units along the Positive Y Axis
Now imagine lifting the rectangle up and pushing it from quadrant 2 into quadrant 1 - i.e, a 90 degree rotation clockwise about the Origin
This would give us a rectangle of 2 units along the positive X axis and 3 units along positive Y axis. Point A would now move to the upper right corner of this new rectangle that we pushed over ———> this will be point (2 , 3)
You can confirm visually by:
-connecting original point A at (-3 ,2) with the Origin
-and connecting new image point A at (2 , 3)
these 2 points and the origin will create a 90 degree angle about the Origin (both lines are diagonals of their respective rectangles)
Or, the explanation is too long winded, you can follow the Rule:
For 90 degree rotations clockwise about the Origin: (X , Y) ———>becomes image point of (Y , -X)
(-3 ,2) becomes (2, 3)
So the first rotation gives us point (2 , 3)
Reflection 2:
Line Y = X is the Line that passes through the origin and creates a 45 degree angle with the X axis
The original point of (2 , 3) and the Image Point will always be equidistant from the Mirror Line over which the original point is reflected.
To visualize it in this problem:
(2 ,2) and (3 , 3) are both on line Y = X
Point (2 , 3) will be +1 unit above (2 ,2) and + 1 unit to the left of (3 , 3)
This creates a right triangle with sides of 1 and 1
To find the image point reflected over Y = X, we make the opposite moves from these points (reversed) on Line Y = X:
from (2 , 2) we move 1 unit to the right: X coordinate = 3
From (3 , 3) we move 1 unit down: Y coordinate = 2
Final Point is (3 , 2)
Or the rule:
Reflecting point (X , Y) over the line given by Y = X ————> image point will be (Y , X)
In other words, just rearrange the coordinates
Answer E
Posted from my mobile device