Exploring Dilation on a Grid

Front

What is dilation in geometry?

Back

Dilation is a transformation that alters the size of a shape but keeps its proportions the same. It is defined by a center point and a scale factor.

Front

What is a scale factor in dilation?

Back

The scale factor is a number that describes how much a shape is enlarged or reduced during a dilation. A scale factor greater than 1 enlarges the shape, while a scale factor between 0 and 1 reduces it.

Front

If a triangle with vertices at (0, 0), (0, 3), and (3, 0) is dilated by a factor of 4, what are the new coordinates of the vertex at (3, 0)?

Back

The new coordinates are (12, 0).

Front

What happens to a shape when it is dilated by a scale factor of 1?

Back

The shape remains unchanged.

Front

What is the dilation rule for a point (x, y) when dilated by a factor of k?

Back

The dilation rule is (kx, ky).

Front

How do you determine if an image has been enlarged or reduced after dilation?

Back

Compare the original dimensions of the shape to the dimensions of the dilated shape. If the new dimensions are larger, it is enlarged; if smaller, it is reduced.

Front

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

Back

A negative scale factor not only changes the size of the shape but also reflects it across the center point.

Front

If a rectangle is dilated so that one vertex moves from (2, 3) to (4, 6), what could be the dilation rule?

Back

The dilation rule could be (2x, 2y).

Front

What does it mean for a shape to be similar after dilation?

Back

Two shapes are similar if they have the same shape but not necessarily the same size, which is a property preserved in dilation.

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.