line q y-2x=6 is transformed by a dilation with a scale factor of 2/3 and centered at the origin. what is the equation of line q after the dilation?
To find the equation of line q after the dilation, we can follow these steps:
Step 1: Start with the original equation of line q: y - 2x = 6
Step 2: Apply the dilation with a scale factor of 2/3. Since the dilation is centered at the origin, it means that only the x and y coordinates of each point on the line will be affected. The scale factor of 2/3 means that the x and y coordinates will be multiplied by 2/3.
Step 3: Apply the dilation to the equation. We need to multiply the x and y terms by 2/3:
- For the x term, we have -2x. After dilation, it becomes -(2/3)x.
- For the y term, we have y. After dilation, it becomes (2/3)y.
Step 4: Rewrite the equation with the dilated terms:
The equation of line q after the dilation is (2/3)y - (2/3)x = 6.
Therefore, the equation of line q after the dilation with a scale factor of 2/3 and centered at the origin is (2/3)y - (2/3)x = 6.