Dilations in the Coordinate Plane

Front

What is a dilation in the coordinate plane?

Back

A dilation is a transformation that alters the size of a figure but not its shape, using a scale factor and a center of dilation.

Front

What is the scale factor in a dilation?

Back

The scale factor is the ratio of a length of the new figure to the corresponding length on the original figure.

Front

If a dilation has a scale factor of 1/2, what type of transformation is it?

Back

It is a reduction.

Front

What happens to the coordinates of a point (x, y) when it is dilated with a scale factor k?

Back

The new coordinates will be (kx, ky).

Front

What is the center of dilation?

Back

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

Front

State the coordinates of the image of point C (4, 2) after a dilation with a scale factor of 1/2 and center point P (0, 0).

Back

(2, 1) because (0.5*4, 0.5*2) = (2, 1).

Front

True or False: A dilation with a scale factor greater than one results in an enlargement.

Back

True.

Front

What is the algebraic representation for a dilation with a scale factor of 3?

Back

(x, y) → (3x, 3y).

Front

If point B (-10, -6) is dilated with a scale factor of 1/2, what are the new coordinates?

Back

(-5, -3) because (0.5*-10, 0.5*-6) = (-5, -3).

Front

What is the effect of a dilation with a scale factor of 1?

Back

The figure remains unchanged.