Scale Factor and Dilations coordinate plane

Front

What is a scale factor?

Back

A scale factor is a number that scales, or multiplies, some quantity. In geometry, it is the ratio of the length of a side of a scaled figure to the length of the corresponding side of the original figure.

Front

What does dilation mean in geometry?

Back

Dilation is a transformation that produces an image that is the same shape as the original, but is a different size. It involves a scale factor and a center of dilation.

Front

If a triangle is dilated by a scale factor of 2, what happens to its size?

Back

The triangle will be enlarged, making each side twice as long as the corresponding side in the original triangle.

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 during a dilation.

Front

How do you find the coordinates of a dilated point?

Back

To find the coordinates of a dilated point, multiply the original coordinates by the scale factor. For example, if the original point is (x, y) and the scale factor is k, the new coordinates will be (kx, ky).

Front

What is the rule for a dilation with a scale factor of 1/2?

Back

The rule for a dilation with a scale factor of 1/2 is given by: @@(x,y) ightarrow igg(rac{1}{2}x, rac{1}{2}yigg)@@.

Front

What is a scale drawing?

Back

A scale drawing is a representation of an object that is either enlarged or reduced in size, maintaining the same proportions as the original.

Front

If a shape is reduced by a scale factor of 1/4, what does that mean?

Back

It means that each side of the shape is multiplied by 1/4, making the new shape one-fourth the size of the original.

Front

What is the effect of a negative scale factor?

Back

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

Front

How do you determine the scale factor from a small shape to a larger shape?

Back

To determine the scale factor, divide the length of a side of the larger shape by the length of the corresponding side of the smaller shape.