Similar shapes and dilation Questionbank

A point $P(6, -4)$ is dilated with the origin $(0, 0)$ as the center and a scale factor of $r = \frac{1}{2}$. The coordinates of the image $P'$ are:

In the general coordinate rule $(x, y) \longmapsto (a+r(x-a), b+r(y-b))$, if the scale factor $r$ is equal to $1$, the transformation is equivalent to:

In a dilation centered at point $C$, the distance from $C$ to a point $P$ is $12\text{ units}$. If the scale factor of the dilation is $r = -\frac{1}{3}$, what is the distance from $C$ to the image $P'$?

The scale factor of a dilation is $r = -0.4$. Which of the following statements best describes the transformation of the figure?

Two similar triangles have perimeters in the ratio $2:5$. If the area of the smaller triangle is $16 \text{ units}^2$, the area of the larger triangle is _____.

A square has vertices at $(0,0), (2,0), (2,2)$, and $(0,2)$. It is dilated with a scale factor of $r = 2$ using the point $(1,1)$ as the center. What is the coordinate of the image of the vertex $(2,2)$?

If the side length of a cube is increased by $20\%$, the volume of the cube increases by _____.

True or False: If two triangles have two pairs of corresponding angles that are equal, they must be similar.

True or False: If a rectangle is dilated by a scale factor $r$, its interior angles will be multiplied by $|r|$.

A cube is dilated such that its total surface area is increased by $300\%$. The volume of the cube increases by a factor of _____.