Question

The coordinates of ADEF are D(-4,4), E(2, 4), and F(0, 2). The triangle is dilated with a scale factor z and center O. What are the coordinates of the vertices of the image of ADEF?

Options:
a) D(-4z,4z), E(2z, 4z), F(0, 2z)
b) D(-4z,4z), E(2z, 4), F(0, 2z)
c) D(-4,4), E(2, 4), F(0, 2)
d) D(-4z,4), E(2z, 4z), F(0, 2)

Answer 1

The coordinates of the vertices of the image of triangle ADEF after dilation with scale factor z and center at the origin are D(-4z,4z), E(2z,4z), and F(0,2z).

Step-by-step explanation:

When a geometric figure is dilated with a scale factor and the center of dilation is the origin (0,0), each coordinate of the figure is multiplied by the scale factor. The given coordinates of triangle ADEF are D(-4,4), E(2, 4), and F(0, 2). To find the image of this triangle after dilation with a scale factor of z, each of the x and y coordinates shall be multiplied by z:

• For point D(-4,4), the dilated coordinates will be D'(-4z, 4z).
• For point E(2, 4), the dilated coordinates will be E'(2z, 4z).
• For point F(0, 2), the dilated coordinates will be F'(0z, 2z), which simplifies to F'(0, 2z).

Therefore, the coordinates of the vertices of the image of ADEF after dilation are D(-4z,4z), E(2z,4z), and F(0,2z).