Question

AXYZ has vertices at (0.0), (6,9), and (15.0).

Y (6,9)
X (0, 0)
Z (15, 0)
AXYZ is dilated by a scale factor of
about the origin.
What are the coordinates of the vertices of the image?
OA (0,0).(2,3), (5.0)
OD. (0,0).(8,12).(20,0)
OR ( }).2.3), (55)
OE ( ).(8,12), (20,3)
Oc (0.01.(4.0) (10,0)

Answer 1

The coordinates of the vertices of the image are (0, 0), (2, 3), (5, 0) ⇒ (A)

Explanation:

Let us talk about dilation

• A dilation is a transformation that changes the size of a figure.
• It can become larger or smaller, but the shape of the figure does not change.
• The scale factor measures how much larger or smaller the image will be
• If the scale factor greater than 1, then the image will be larger
• If the scale factor between 0 and 1, then the image will be smaller

→ If point (x, y) dilated with scale factor m about the origin, then

→ Its image is (m x, m y)

Let us solve the question

∵ ΔXYZ has vertices:

→ X = (0, 0)

→ Y = (6, 9)

→ Z = (15, 0)

∵ ΔXYZ is dilated by a scale factor 1/3 about the origin

→ Multiply each coordinate in each vertex by the scale factor 1/3

∵ (0 ×
`(1)/(3)` , 0 ×
`(1)/(3)` )

∴ X' = (0, 0)

∵ (6 ×
`(1)/(3)` , 9 ×
`(1)/(3)` )

∴ Y' = (2 , 3)

∵ (15 ×
`(1)/(3)` , 0 ×
`(1)/(3)` )

∴ Z' = (5, 0)

∴ The coordinates of the vertices of the image are (0, 0), (2, 3), (5, 0)