Question

The line represented by the equation 4y = 3x + 7 is transformed by a dilation centered at the origin. Which linear equation could represent its image? (1) 3x - 4y = 9 (2) 3x + 4y = 9 (3) 4x - 3y = 9 (4) 4x + 3y = 9

Answer 1

The mirror image of a line about origin will be obtained by replacing x with -x and y with -y.

Therefore, the mirror image of the line 4y = 3x + 7 will be:

`\begin{gathered} 4(-y)=3(-x)+7 \\ -4y=-3x+7 \end{gathered}`

Rearranging the equation, we have:

`3x-4y=7`

Note that a dilation always preserves parallelism. Therefore, any image formed from the preimage must have the same slope.

Therefore, we can say that the dilation will yield the equation:

`3x-4y=k`

where k is a constant.

Going by this, the equation that can represent its image will be:

`3x-4y=9`

OPTION 1 is correct.