A triangle has vertices at A(–2, 4), B(–2, 8), and C(6, 4). If A prime 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 scale factor is One-eighth

The coordinates of C prime are (0.75, 0.5).

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

Step-by-step explanation:

A triangle has vertices at A(–2, 4), B(–2, 8), and C(6, 4). If A prime 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 prime are (0.75, 0.5). The coordinates of C prime are (1.5, 1). The scale factor is One-eighth. The scale factor is 8. The scale factor is One-fourth. The scale factor is 4. The coordinates of B prime are (–0.25, 1). The coordinates of B prime are (–0.5, 2).

Solution:

Transformation is the movement of a point from its initial location to a new location. If an object is transformed then all its points are also transformed. Types of transformation are reflection, dilation, rotation and translation.

Dilation is the enlargement or reduction in size of an object. If a point X(x, y)  is dilated about the origin by a factor k, its new location is X'(kx, ky)

Triangle ABC with vertices at A(–2, 4), B(–2, 8), and C(6, 4) is dilated to give A'(-0.25, 0.5)

kA = A'

(-2k, 4k) = (-0.25, 0.5)

-2k = -0.25, hence k = 1/8

Therefore the scale factor is 1/8 (one- eight)

The new location of the vertices is B'(-0.25, 1), C'(0.75, 0.5)

236 cm 16 time 12 = 192

6 times 7 = 42

192+42