A triangle's coordinates are (-2,1), (-6,1), and (-4, 5). After the triangle is rotated clockwise 270°about the origin, what are the new coordinates?
well, the initial x coordinates become the -y coordinates, the y coordinates become the +x
example (-4, 5) becomes (5,4)
the triangle starts out in Quad IV , and ends up in Quad III
try a test point to see what happens
the x's become y's , and the y's become negative x's
bob, did you rotate far enough?
To find the new coordinates after rotating the triangle clockwise by 270° about the origin, you can follow these steps:
Step 1: Find the new coordinates of each vertex separately.
Step 2: Apply the rotation formula to each vertex.
The rotation formula for a point (x, y) counterclockwise by an angle θ about the origin (0, 0) is:
New_x = x * cos(θ) - y * sin(θ)
New_y = x * sin(θ) + y * cos(θ)
In this case, since we want to rotate the triangle clockwise, we can use the same formula but with a negative angle (-270°), which is equivalent to rotating it clockwise by 270°.
Let's apply the rotation formula to each vertex of the triangle:
Vertex A (-2, 1):
Using the formula:
New_x = -2 * cos(-270°) - 1 * sin(-270°)
New_y = -2 * sin(-270°) + 1 * cos(-270°)
Simplifying further:
New_x = 1
New_y = -2
So the new coordinates for vertex A are (1, -2).
Vertex B (-6, 1):
Using the formula:
New_x = -6 * cos(-270°) - 1 * sin(-270°)
New_y = -6 * sin(-270°) + 1 * cos(-270°)
Simplifying further:
New_x = -1
New_y = -6
So the new coordinates for vertex B are (-1, -6).
Vertex C (-4, 5):
Using the formula:
New_x = -4 * cos(-270°) - 5 * sin(-270°)
New_y = -4 * sin(-270°) + 5 * cos(-270°)
Simplifying further:
New_x = 5
New_y = -4
So the new coordinates for vertex C are (5, -4).
Therefore, the new coordinates of the triangle after rotating clockwise 270° about the origin are:
A (1, -2),
B (-1, -6), and
C (5, -4).