Question

Using matrix methods, how to find the image of the point `((1), (-2))` under each of the following transformations?: 1) dilation of the factor 3 from the x-axis 2) reflection in the y-axis

Answer 1

See the explanation below

Explanation:

The matrix for the dilation by a factor `3` from the x-axis is

`A=((1,0),(0,3))`

Therefore, the image is

`((x'),(y'))=A*((1),(-2))=((1,0),(0,3))*((1),(-2))=((1),(-6))`

The image of `(1,-2)` by a dilation factor `3` from the x-axis is `(1,-6)`

The matrix for the reflection in the y-axis is

`B=((-1,0),(0,1))`

Therefore, the image is

`((x'),(y'))=B*((1),(-2))=((-1,0),(0,1))*((1),(-2))=((-1),(-2))`

The image of the point `(1,-2)` by a reflection in the y-axis is `(-1,-2)`