Question:
1) Blue triangle points; (-1, 4), (-5, 4), and (-1, 1)
Red triangle points; (-4, -1), (-1, -1). and (-4, -5)
2) Blue triangle points (1, 1), (4, 5), (4, 1)
Red triangle points; (-1, 1), (-1, 4). and (-5, 4)
3) Blue triangle points (0, 1), (4, 4), (4, 1)
Red triangle points; (-4, 1), (-4, 4). and (0, 1)
4) Blue triangle points (-5, 4), (-1, 4), (-1, 1)
Red triangle points; (1, 1), (4, 1). and (4, 5)
5) Blue triangle points (-2, 5), (4, 5), (4, 1)
Red triangle points; (-1, 4), (-5, 4). and (-5, -2)
Answer:
The correctly rotated red triangles are those of (1), (2), and (5)
Step-by-step explanation:
In a 90° counterclockwise rotation, every x and y points of the original triangle are switched while the y is turned negative, as shown in the following equation;
(x, y) to (-y, x)
Therefore, the triangles that undergo a 90° counterclockwise rotation are as follows;
1) Blue triangle points; (-1, 4), (-5, 4), and (-1, 1)
Red triangle points; (-4, -1), (-1, -1). and (-4, -5)
(-1, 4) → (-4, -1)
(-5, 4) → (-4, -5)
(-1, 1) → (-1, -1)
Correctly rotated 90° counterclockwise
2) Blue triangle points (1, 1), (4, 5), (4, 1)
Red triangle points; (-1, 1), (-1, 4). and (-5, 4)
(1, 1) → (-1, 1)
(4, 5) → (-5, 4)
(4, 1) → (-1, 4)
Correctly rotated 90° counterclockwise
3) Blue triangle points (0, 1), (4, 4), (4, 1)
Red triangle points; (-4, 1), (-4, 4). and (0, 1)
(0, 1) → (0, 1) ≠ (-1, 0)
(4, 4) → (-4, 4)
(4, 1) → (-4, 1)
Not correctly rotated 90° counterclockwise
4) Blue triangle points (-5, 4), (-1, 4), (-1, 1)
Red triangle points; (1, 1), (4, 1). and (4, 5)
(-5, 4) → (4, 5) ≠ (-4, -5)
(-1, 4) → (4, 1)
(-1, 1) → (1, 1)
Not correctly rotated 90° counterclockwise
5) Blue triangle points (-2, 5), (4, 5), (4, 1)
Red triangle points; (-1, 4), (-5, 4). and (-5, -2)
(-2, 5) → (-5, -2)
(4, 5) → (-5, 4)
(4, 1) → (-1, 4)
Correctly rotated 90° counterclockwise.
