Dilation & Scale Factor

Front

What is dilation in geometry?

Back

Dilation is a transformation that alters the size of a figure but not its shape. It involves a center of dilation and a scale factor.

Front

What is a scale factor?

Back

The scale factor is a number that scales, or multiplies, the dimensions of a figure during dilation. It can be greater than 1 (enlargement) or between 0 and 1 (reduction).

Front

If a point A(x, y) is dilated by a scale factor of k, what are the new coordinates of A'?

Back

The new coordinates A' are given by (kx, ky).

Front

What happens to the coordinates of a triangle's vertices when it is dilated by a scale factor of 3?

Back

Each vertex (x, y) of the triangle will be transformed to (3x, 3y).

Front

How do you find the coordinates of a dilated image if the center of dilation is the origin?

Back

Multiply each coordinate of the original figure by the scale factor.

Front

What is the formula for calculating the scale factor when given the old and new dimensions?

Back

Front

If triangle ABC has vertices A(2, 3), B(4, 5), and C(6, 7), what are the coordinates after a dilation by a scale factor of 1/2?

Back

The new coordinates will be A'(1, 1.5), B'(2, 2.5), C'(3, 3.5).

Front

What is the effect of a scale factor less than 1 on a geometric figure?

Back

A scale factor less than 1 reduces the size of the figure, making it smaller.

Front

If a triangle is dilated by a scale factor of 2, what is the relationship between the area of the original triangle and the area of the dilated triangle?

Back

The area of the dilated triangle is 4 times the area of the original triangle (since area scales by the square of the scale factor).

Front

How do you determine the coordinates of a point after dilation if the center of dilation is not the origin?

Back

Use the formula: A' = O + k(A - O), where O is the center of dilation, A is the original point, and k is the scale factor.