Dilation

Front

What is the center of dilation?

Back

The center of dilation is a fixed point in the plane about which all points are expanded or contracted. For example, if the center of dilation is P(-2, 0), all points will move away from or towards this point based on the scale factor.

Front

If ABC is dilated about P(2, -4) by a scale factor of 3, what are the coordinates of B'?

Back

To find the coordinates of B' after dilation, apply the formula: B' = P + k(B - P), where k is the scale factor. If B is at (0, 0), then B' = (2, -4) + 3[(0, 0) - (2, -4)] = (-4, 2).

Front

How do you write the algebraic notation for dilation with a scale factor of 3?

Back

The algebraic notation for dilation with a scale factor of 3 is (x, y) goes to (3x, 3y).

Front

What can you say about the scale factor, k, if it is greater than 1?

Back

If the scale factor k > 1, the dilation is an enlargement, meaning the image will be larger than the original figure.

Front

What can you say about the scale factor, k, if it is less than 1?

Back

If the scale factor 0 < k < 1, the dilation is a reduction, meaning the image will be smaller than the original figure.

Front

What happens when the scale factor k equals 1?

Back

When the scale factor k = 1, the dilation does not change the size of the figure; the image is congruent to the original.

Front

What is the effect of a negative scale factor on dilation?

Back

A negative scale factor reflects the figure across the center of dilation and changes its size. For example, a scale factor of -2 will double the size and flip the figure.

Front

If a point A(1, 2) is dilated about the origin (0, 0) by a scale factor of 2, what are the new coordinates of A'?

Back

The new coordinates of A' after dilation will be A' = (2*1, 2*2) = (2, 4).

Front

What is the relationship between the original figure and its image after dilation?

Back

The original figure and its image after dilation are similar; they have the same shape but may differ in size depending on the scale factor.

Front

How do you determine the coordinates of a point after dilation about a point other than the origin?

Back

To determine the coordinates of a point after dilation about a point P(a, b), use the formula: A' = P + k(A - P), where A is the original point and k is the scale factor.