Dilations in the Coordinate Plane

A quadrilateral with vertices at A(4, –4), B(4, –16), C(12, –16), and D(12, –4) has been dilated with a center at the origin. The image of D, point D' , has coordinates (36, –12). What is the scale factor of the dilation?

Segment AB is being dilated with the center at the origin. The image of A, point A', has coordinates of (3.2, 6.4). What is the scale factor of the dilation and the coordinates of point B'?

• The scale factor is 0.8 and the coordinates of point B' are (–3.2, –4.8).

• The scale factor is 1.25 and the coordinates of point B' are (–3.2, –4.8).

• The scale factor is 0.8 and the coordinates of point B' are (–5, –7.5).

• The scale factor is 1.25 and the coordinates of point B' are (–5, –7.5).

Triangle ABC is being dilated with the center of dilation at the origin. The image of C, point C' , has coordinates of (7.2, 3.6). What is the scale factor of the dilation and what are the coordinates of point A' ?

• The scale factor is 1.2 and the coordinates of point A' are (–2.5, 2.5).

• The scale factor is 5/6 and the coordinates of point A' are (–2.5, 2.5).

• The scale factor is 1.2 and the coordinates of point A' are (–3.6, 3.6).

• The scale factor is 5/6 and the coordinates of point A' are (–3.6, 3.6).

The rectangle is the image after a dilation with the center of dilation at the origin of rectangle ABCD. The pre-image of A', point A, has coordinates of (–4, 3.2). What is the scale factor of the dilation and what are the coordinates of point C?

• The scale factor is 2.5 and the coordinates of point C are (–2.4, –0.8).

• The scale factor is 0.4 and the coordinates of point C are (–2.4, –0.8).

• The scale factor is 2.5 and the coordinates of point C are (–15, 5).

• The scale factor is 0.4 and the coordinates of point C are (–15, 5).

A triangle has vertices at A(–2, 4), B(–2, 8), and C(6, 4). If A' has coordinates of (–0.25, 0.5) after the triangle has been dilated with a center of dilation about the origin, which statements are true? Check all that apply.

• The coordinates of C' are (0.75, 0.5).

• The scale factor is 1/8

• The coordinates of B' are (–0.25, 1).

• The scale factor is 8.

• The scale factor is 4.

What is the scale factor of a triangle with a vertex of A(–6, 4) that has been dilated with a center of dilation at the origin so the vertex of its image is A' (–24, 16)?

The image of a triangle after it has been dilated with a center at the origin has vertices at A' (–12, 6), B' (6, –18), and C'. If the pre-image of A', point A, has coordinates of (–18, 9) and the pre-image of C', point C, has coordinates of (18, 12), which statements are true? Check all that apply

• The coordinates of C' are (12, 8).

• The scale factor is 2/3

• The coordinates of B are (9, –27).

• The coordinates of B are (4, –12).

• The scale factor is 1.5.

A triangle has vertices A(0,0), B(8,0), C(3,-2). Find the coordinates of the triangle after a dilation with a scale factor of  4. The dilation is (X,Y) --- (4x,4y)

• A(3,3), B(4,4), C(-3,-4)

• A(-4,8), B(6.5,8), C(7,7)

• A(0,0), B(32,0), C(12,-8)

Dilate Point B by a scale factor of 1/2

• (1.5,-4)

• (-1.5,1)

• (-1,-1.5)

• (-2,-2)

Triangle ABC is dilated using a scale factor of 1/2. What are the new coordinates of point A'?

• (-3, 3)

• (-12, 12)

• (-2, 2)