Translations and Reflections

Front

What is a translation in geometry?

Back

A translation is a transformation that moves every point of a figure the same distance in a specified direction.

Front

How do you translate a point (x, y) to the left by 7 units?

Back

To translate a point (x, y) to the left by 7 units, you subtract 7 from the x-coordinate: (x-7, y).

Front

What is the reflection of a point (x, y) over the x-axis?

Back

The reflection of a point (x, y) over the x-axis is (x, -y).

Front

What is the reflection of a point (x, y) over the y-axis?

Back

The reflection of a point (x, y) over the y-axis is (-x, y).

Front

If Point A is at (3, -8), what are the coordinates after translating it to A'(-4, -5)?

Back

The translation is (x-7, y+3).

Front

What is the formula for finding the midpoint between two points A(x1, y1) and B(x2, y2)?

Back

The midpoint M is given by M = ((x1 + x2)/2, (y1 + y2)/2).

Front

How do you find a point that divides a line segment in a given ratio?

Back

Use the formula P = ((mx2 + nx1)/(m+n), (my2 + ny1)/(m+n)) where P divides AB in the ratio m:n.

Front

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

Back

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

Front

What is the result of reflecting the point (9, -2) over the x-axis?

Back

The result is (9, 2).

Front

If a triangle is translated 2 units left, how do you find the new coordinates of its vertices?

Back

Subtract 2 from the x-coordinate of each vertex.