Transformations and similarity quick check
1. Identify the transformation:
Given points A(3, 2) and B(5, 4), the coordinates of the points after a translation by (-1, -1) would be:
Solution:
A' = A + (-1, -1)
= (3, 2) + (-1, -1)
= (3 + (-1), 2 + (-1))
= (2, 1)
B' = B + (-1, -1)
= (5, 4) + (-1, -1)
= (5 + (-1), 4 + (-1))
= (4, 3)
Therefore, the new coordinates of A and B after the translation are A'(2, 1) and B'(4, 3).
2. Identify the transformation:
Given triangle ABC with coordinates A(2, 3), B(4, 5), and C(6, 1), the triangle after a reflection over the x-axis would have the following coordinates:
Solution:
A' = (x, y) → A' = (x, -y)
= (2, 3) → A' = (2, -3)
B' = (x, y) → B' = (x, -y)
= (4, 5) → B' = (4, -5)
C' = (x, y) → C' = (x, -y)
= (6, 1) → C' = (6, -1)
Therefore, the new coordinates of triangle ABC after the reflection over the x-axis are A'(2, -3), B'(4, -5), and C'(6, -1).
3. Identify the transformation:
Given point P(3, 2), the coordinates of the point after a dilation with a scale factor of 2 centered at the origin would be:
Solution:
P' = scale factor * P
= 2 * (3, 2)
= (2 * 3, 2 * 2)
= (6, 4)
Therefore, the new coordinates of point P after the dilation with a scale factor of 2 centered at the origin are P'(6, 4).
4. Identify the transformation:
Given triangle ABC with coordinates A(2, 2), B(5, 2), and C(4, 4), the triangle after a rotation of 90 degrees counterclockwise around the origin would have the following coordinates:
Solution:
A' = (x, y) → A' = (-y, x)
= (2, 2) → A' = (-2, 2)
B' = (x, y) → B' = (-y, x)
= (5, 2) → B' = (-2, 5)
C' = (x, y) → C' = (-y, x)
= (4, 4) → C' = (-4, 4)
Therefore, the new coordinates of triangle ABC after the rotation of 90 degrees counterclockwise around the origin are A'(-2, 2), B'(-2, 5), and C'(-4, 4).