7.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:
d. Rx = 3
e. T<3,-6>
f. r(90◦, o)
I did already post this, but I forgot to bookmark it. I know Scott replied, but it ended up not helping me. Please help! I would greatly appreciate it!
sOrRy mY cAt rAn oVeR mY kEy bOarD ;)
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To find the vertices of ∆ABC after each transformation, we can apply the corresponding transformation rules to each vertex of the original triangle.
d. Rx = 3:
To perform a reflection in the x-axis, we need to negate the y-coordinate of each vertex while keeping the x-coordinate unchanged.
The transformation rule is: (x, y) → (x, -y)
Applying this rule to each vertex of ∆ABC:
A (2, -5) → (2, -(-5)) = (2, 5)
B (-4, 6) → (-4, -6)
C (3, 1) → (3, -1)
So, the vertices after reflection in the x-axis are A' (2, 5), B' (-4, -6), and C' (3, -1).
e. T<3, -6>:
To perform a translation, we need to add the given translation vector to each vertex of the original triangle.
The transformation rule is: (x, y) → (x + Δx, y + Δy)
Applying this rule to each vertex of ∆ABC:
A (2, -5) → (2 + 3, -5 + (-6)) = (5, -11)
B (-4, 6) → (-4 + 3, 6 + (-6)) = (-1, 0)
C (3, 1) → (3 + 3, 1 + (-6)) = (6, -5)
So, the vertices after the translation T<3, -6> are A' (5, -11), B' (-1, 0), and C' (6, -5).
f. r(90°, o):
To perform a rotation, we need to apply the rotation matrix to each vertex of the original triangle.
The transformation rule is:
(x, y) → (x*cosθ - y*sinθ, x*sinθ + y*cosθ)
Where θ is the angle of rotation.
Applying this rule to each vertex of ∆ABC, with θ = 90°:
A (2, -5) → (2*cos90° - (-5)*sin90°, 2*sin90° + (-5)*cos90°) = (-5, 2)
B (-4, 6) → (-4*cos90° - 6*sin90°, -4*sin90° + 6*cos90°) = (-6, -4)
C (3, 1) → (3*cos90° - 1*sin90°, 3*sin90° + 1*cos90°) = (-1, 3)
So, the vertices after rotation r(90°, o) are A' (-5, 2), B' (-6, -4), and C' (-1, 3).
Please note that the original response might have different values due to randomization by the AI system.