Dilations and Scale Factors: Practice Level 3 | Geometry

Level 3 · Challenge 0 / 12 answered

Question 1 of 12

1

One dilation sends $P(1, 2)$ to $P'(4, 5)$ and $Q(4, 2)$ to $Q'(10, 5)$ . What are its scale factor and center?

Answer choices for question 1 A $2$ ; center $(2,1)$ B $3$ ; center $(0,0)$ C $\frac12$ ; center $(-2,-1)$ D $2$ ; center $(-2,-1)$
2

A proposed dilation fixes two distinct points but moves a third point. Which conclusion follows?

Answer choices for question 2 A Its center is the midpoint of the fixed points B No dilation can have all three stated effects C Its factor is 2 D Its factor is 1 and it moves only the third point
3

A dilation centered at $(0,-1)$ sends the line $y=2$ onto the line $y=5$ . What is its scale factor?

Answer choices for question 3 A $2$ B $\frac52$ C $3$ D $\frac12$
4

A figure is dilated about $O$ by $\frac 23$ , then the image is dilated about the same $O$ by $\frac 32$ . What is the overall effect?

Answer choices for question 4 A Every point moves half as far from O B Only O returns C Every point returns to its original location D Lengths return but angles do not
5

Which point is the center of the dilation $(x,y)\mapsto(3x-4, 3y+2)$ ?

Answer choices for question 5 A $(2,-1)$ B $(-4,2)$ C $(-2,1)$ D $(0,0)$
6

The rule $(x,y)\mapsto(2x,3y)$ acts on $O(0, 0)$ , $A(3, 0)$ and $B(0, 2)$ . Why can these three images not come from one dilation?

Answer choices for question 6 A The origin is fixed B The images stay on the rays from O C The angle at O stays a right angle D OA requires factor 2, while OB requires factor 3
7

Can a positive dilation centered at the origin send $(-2, 0)$ to $(6, 0)$ ?

Answer choices for question 7 A Yes, with factor 3 B No, the two points lie on opposite rays from the center C Yes, with factor one third D Yes, with factor 4
8

The identity map is described as a dilation with scale factor $1$ . What can be said about its center?

Answer choices for question 8 A Its center must be the origin B Its center is uniquely determined by any image point C Any point can serve as its center D It has no possible center
9

A dilation with center $(t,-1)$ and scale factor $2$ sends $(4, 3)$ to $(10, 7)$ . Find $t$ .

Answer choices for question 9 A $2$ B $6$ C $-6$ D $-2$
10

A claimed dilation centered at the origin sends $(1, 0)$ to $(2, 0)$ and $(0, 1)$ to $(0, 3)$ . Which assessment is correct?

Answer choices for question 10 A It fails because the two point mappings require different scale factors B It is valid because both image points stay on the correct rays C It is valid with factor 5 D It fails because the center would have to move
11

A dilation with factor $2$ and center $(a,b)$ maps the entire horizontal line $y=6$ onto itself. What must be true?

Answer choices for question 11 A $a=6$ B $b=0$ C $b=6$ D $a=b$
12

A dilation has factor $2$ . A side of length $p+1$ has an image of length $3p-1$ . An original angle measures $62^\circ$ . Which pair gives $p$ and the image angle measure?

Answer choices for question 12 A $3$ and $124^\circ$ B $3$ and $62^\circ$ C $1$ and $62^\circ$ D $2$ and $31^\circ$