Transformations

Front

What is a transformation in geometry?

Back

A transformation is an operation that moves or changes a shape in some way on a coordinate plane.

Front

What are the four main types of transformations?

Back

The four main types of transformations are translation, rotation, reflection, and dilation.

Front

How do you translate a point (x, y) 2 units to the right and 3 units up?

Back

The new coordinates will be (x+2, y+3).

Front

What happens to the coordinates of a point when it is reflected across the x-axis?

Back

The y-coordinate changes sign, so (x, y) becomes (x, -y).

Front

If point A(2, 3) is translated 4 units left and 1 unit down, what are the new coordinates?

Back

The new coordinates are (-2, 2).

Front

What is the result of reflecting the point (5, -7) across the y-axis?

Back

The new coordinates will be (-5, -7).

Front

How do you perform a rotation of 90 degrees counterclockwise around the origin?

Back

The new coordinates (x, y) become (-y, x).

Front

What is the effect of a dilation with a scale factor of 2 on the point (3, 4)?

Back

The new coordinates will be (6, 8).

Front

If triangle ABC has vertices A(1, 2), B(3, 4), and C(5, 6), what are the coordinates after a translation of (2, -3)?

Back

The new coordinates will be A(3, -1), B(5, 1), C(7, 3).

Front

What is the formula for translating a point (x, y) by (a, b)?

Back

The new coordinates will be (x+a, y+b).