Given the vertices of ∆ABC are A (2,-5), B (-4,6) and C (3,1), find the vertices following each of the transformations FROM THE ORIGINAL vertices:
1)• Rx = 3
2)• T<3,-6>
3)• r(90◦, o)
Please help!
I am not familiar with your notations.
e.g.
• T<3,-6> ?????
I'm not sure. Its whats what teacher wants. I've never seen anything like it.
I have my doubts that your teacher would use a notation or a concept that was never taught to you. What does your text say? Did you not attend your classes ?
i think ...
1)Reflection over x=3
2) Translation ... 3 in x , -6 in y
3) rotation ... 90º about the origin
I do online school. I don't really have a teacher. Thankyou Scott.
To find the vertices after each transformation, we need to apply the corresponding transformations to each of the original vertices. Let's go through each transformation one by one:
1) Rx = 3: This transformation represents a reflection across the x-axis.
To perform this transformation, we need to negate the y-coordinate of each vertex while keeping the x-coordinate the same.
So the new vertices after this transformation will be:
A' = (2, 5)
B' = (-4, -6)
C' = (3, -1)
2) T <3, -6>: This transformation represents a translation.
To perform this transformation, we need to add the given values to the x-coordinate and y-coordinate of each vertex.
So the new vertices after this transformation will be:
A' = (2 + 3, -5 - 6) = (5, -11)
B' = (-4 + 3, 6 - 6) = (-1, 0)
C' = (3 + 3, 1 - 6) = (6, -5)
3) r(90°, o): This transformation represents a rotation of 90 degrees counterclockwise about the origin.
To perform this transformation, we need to use the rotation formula:
x' = x * cos(θ) - y * sin(θ)
y' = x * sin(θ) + y * cos(θ)
where θ is the angle of rotation (90° in this case).
Applying the formula to each vertex, we get:
A' = (2 * cos(90°) - (-5) * sin(90°), 2 * sin(90°) + (-5) * cos(90°)) = (5, 2)
B' = (-4 * cos(90°) - 6 * sin(90°), -4 * sin(90°) + 6 * cos(90°)) = (-6, 4)
C' = (3 * cos(90°) - 1 * sin(90°), 3 * sin(90°) + 1 * cos(90°)) = (-1, 3)
So the new vertices after this transformation will be:
A' = (5, 2)
B' = (-6, 4)
C' = (-1, 3)
That's it! These are the vertices after each of the given transformations.