Question

Given the preimage and image,find the dilation scale factor.​

Answer 1

The dilation scale factor is
`(1)/(2)`.

Explanation:

The image is the dilated form of its preimage if and only if the following conditions are observed:

1)
`K' = \alpha_(1) \cdot K`

2)
`T' = \alpha_(2) \cdot T`

3)
`P' = \alpha_(3) \cdot P`

4)
`J' = \alpha_(4) \cdot J`

5)
`\alpha_(1) = \alpha_(2) = \alpha_(3) = \alpha_(4)`

If we know that
`K = (2, 0)`,
`K' = (1, 0)`,
`T = (3, 0)`,
`T' = (1.5,0)`,
`P = (1, 5)`,
`P' = (0.5, 2.5)`,
`J = (0, 3)` and
`J' = (0, 1.5)`, then the coefficients are, respectively:

`\alpha_(1) = (1)/(2)`,
`\alpha_(2) = (1)/(2)`,
`\alpha_(3) = (1)/(2)`,
`\alpha_(4) = (1)/(2)`

As
`\alpha_(1) = \alpha_(2) = \alpha_(3) = \alpha_(4)`, we conclude that the dilation scale factor applied in the preimage is equal to
`(1)/(2)`.