Geometry Transformations

Front

What is a translation in geometry?

Back

A translation is a type of transformation that moves every point of a shape a constant distance in a specified direction.

Front

How do you perform a translation on a point (x, y)?

Back

To translate a point (x, y) by (a, b), you add a to the x-coordinate and b to the y-coordinate, resulting in (x + a, y + b).

Front

What is the result of translating the point A(-6, -2) by T(-4, 2)?

Back

The image of point A after translation T(-4, 2) is A'(-10, 0).

Front

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

Back

When a point (x, y) is reflected over the x-axis, its coordinates change to (x, -y).

Front

Reflect the point (6, -3) over the x-axis. What is the new point?

Back

The new point after reflection is (6, 3).

Front

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

Back

The formula for translation is (x, y) → (x + a, y + b), where a is the horizontal shift and b is the vertical shift.

Front

Given the point Y(5, 2), what is the result of the translation (x + 2, y - 7)?

Back

The image of point Y after the translation is Y'(7, -5).

Front

How do you determine the translation needed to move triangle ABC to triangle A'B'C'?

Back

To determine the translation, identify the change in x and y coordinates from each vertex of triangle ABC to its corresponding vertex in triangle A'B'C'.

Front

What is the result of reflecting triangle ΔXYZ with vertices X(0, -3), Y(-2, 4), Z(1, 3) over the x-axis?

Back

The reflected triangle has vertices X'(0, 3), Y'(-2, -4), Z'(1, -3).

Front

What is a reflection in geometry?

Back

A reflection is a transformation that flips a shape over a line, creating a mirror image.