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!
To find the vertices following each of the transformations given the original vertices of triangle ABC, follow these steps:
d. Rx = 3 (Reflection across the x-axis)
To reflect a point across the x-axis, you'll need to negate the y-coordinate of each vertex while keeping the x-coordinate unchanged.
Vertex A (2, -5): The x-coordinate stays the same, but negate the y-coordinate: A' = (2, 5)
Vertex B (-4, 6): The x-coordinate stays the same, but negate the y-coordinate: B' = (-4, -6)
Vertex C (3, 1): The x-coordinate stays the same, but negate the y-coordinate: C' = (3, -1)
e. T<3, -6> (Translation by 3 units to the right and 6 units downwards)
To translate a point by a certain number of units along the x-axis and the y-axis, add the given values to the x-coordinate and subtract them from the y-coordinate of each vertex.
Vertex A (2, -5): Add 3 to the x-coordinate and subtract 6 from the y-coordinate: A' = (2 + 3, -5 - 6) = (5, -11)
Vertex B (-4, 6): Add 3 to the x-coordinate and subtract 6 from the y-coordinate: B' = (-4 + 3, 6 - 6) = (-1, 0)
Vertex C (3, 1): Add 3 to the x-coordinate and subtract 6 from the y-coordinate: C' = (3 + 3, 1 - 6) = (6, -5)
f. r(90◦, o) (Rotation of 90 degrees counterclockwise about the origin)
To rotate a point counterclockwise by a certain angle about the origin, you can use the following rotation formula:
x' = x * cosθ - y * sinθ
y' = x * sinθ + y * cosθ
where θ is the angle of rotation.
Vertex A (2, -5):
x' = 2 * cos(90°) - (-5) * sin(90°) = 0 - (-5) = 5
y' = 2 * sin(90°) + (-5) * cos(90°) = 2 + 0 = 2
A' = (5, 2)
Vertex B (-4, 6):
x' = (-4) * cos(90°) - 6 * sin(90°) = 0 - 6 = -6
y' = (-4) * sin(90°) + 6 * cos(90°) = (-4) + 0 = -4
B' = (-6, -4)
Vertex C (3, 1):
x' = 3 * cos(90°) - 1 * sin(90°) = 0 - 1 = -1
y' = 3 * sin(90°) + 1 * cos(90°) = 3 + 0 = 3
C' = (-1, 3)
These are the vertices following each of the transformations Rx = 3, T<3, -6>, and r(90°, o) from the original vertices of triangle ABC.