Consider the line y = x.
If the line is dilated by a factor of 2, what is the equation of the resulting line?
If the resulting line is translated 3 units up, what is the equation of the resulting line?
I would say my answer or guess to this but I legitimately have no idea what this question even means or what they want me to do HELP
You didn’t help at all. What’s the point of u being here
dilation of a line through (0,0) does not change the line in any way.
shifting up is just y+3
I understand that you are unsure about the concepts in the question. Let's break it down step by step.
1. Dilating the line by a factor of 2:
When a line is dilated, its size is changed while maintaining its shape. In this case, a dilation factor of 2 means that every point on the line will be multiplied by 2.
The original equation is y = x. To dilate it by a factor of 2, we need to multiply the x-coordinate by 2. Let's call the dilated line y' = x'.
Therefore, the equation of the dilated line is y' = 2x.
2. Translating the line 3 units up:
Translation refers to shifting the entire line in a specific direction. In this case, we want to shift the line 3 units up.
To achieve this, we need to add 3 to the y-coordinate. So, for the dilated line y' = 2x, we add 3 to the y-coordinate:
y' + 3 = 2x.
Therefore, the equation of the resulting line, after being dilated by a factor of 2 and then translated 3 units up, is y' + 3 = 2x.
Please let me know if there is anything else I can assist you with!