Transformations GEO TEST 24-25

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 given direction.

Front

How do you find the image of a point after a translation using a vector?

Back

To find the image of a point after a translation, add the vector components to the original coordinates. For example, if A(8,9) is translated by the vector <-5, -2>, then A' = (8-5, 9-2) = (3, 7).

Front

What is dilation in geometry?

Back

Dilation is a transformation that alters the size of a figure but not its shape, using a scale factor (K).

Front

How do you calculate the coordinates of a point after dilation?

Back

To calculate the coordinates after dilation, multiply each coordinate of the original point by the scale factor K. For example, if A(10, 3) is dilated with K = 4, then A' = (10*4, 3*4) = (40, 12).

Front

What does the vector represent in transformations?

Back

The vector represents the change in position of a point in a transformation, indicating how much to move in the x-direction and y-direction.

Front

What is the effect of a translation vector of <5, 20>?

Back

A translation vector of <5, 20> moves a point 5 units to the right and 20 units up.

Front

What is the difference between rotation and reflection in transformations?

Back

Rotation turns a figure around a point, while reflection flips a figure over a line.

Front

What is the formula for a translation of a point (x, y) using a vector ?

Back

The formula for translating a point (x, y) using a vector is (x', y') = (x + a, y + b).

Front

What does a scale factor of K = 1 mean in dilation?

Back

A scale factor of K = 1 means that the figure remains the same size after dilation; it does not change.

Front

How do you determine the center of dilation?

Back

The center of dilation is the fixed point in the plane about which all points are expanded or contracted.