Dilations

Front

What is a dilation in geometry?

Back

A dilation is a transformation that alters the size of a figure but keeps its shape the same, using a center of dilation and a scale factor.

Front

What does the scale factor (k) indicate in a dilation?

Back

The scale factor (k) indicates how much the figure is enlarged or reduced. If k > 1, the figure enlarges; if k = 1, the figure remains the same size; if 0 < k < 1, the figure reduces.

Front

What is the effect of a scale factor of 1/2 on a figure?

Back

A scale factor of 1/2 reduces the size of the figure to half of its original dimensions.

Front

Are dilated figures congruent?

Back

No, dilated figures are not congruent unless the scale factor is 1. They are similar but not the same size.

Front

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

Back

To find the coordinates of a point after dilation, multiply the original coordinates by the scale factor and add the coordinates of the center of dilation.

Front

What happens to the coordinates of a point (x, y) when dilated by a scale factor k with center at the origin?

Back

The new coordinates will be (kx, ky).

Front

If a triangle has vertices A(2,0), B(3,-1), and C(-2,-5), what are the new coordinates after dilation by a scale factor of 3?

Back

The new coordinates will be A'(6,0), B'(9,-3), C'(-6,-15).

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

If the center of dilation is at (3, 1) and a point P is at (6, 4), what are the coordinates of P after a dilation with a scale factor of 2?

Back

The new coordinates will be (3 + 2*(6-3), 1 + 2*(4-1)) = (9, 7).

Front

What is the relationship between similar figures and dilations?

Back

Similar figures have the same shape but may differ in size, which is the result of dilations.