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A figure is dilated by a scale factor of 3. If the origin is the center of dilation, what is the image of a vertex located at [tex]$(3,4)$[/tex]?

A. [tex]$(9,4)$[/tex]
B. None of the other answers are correct
C. [tex]$\left(1,1 \frac{1}{2}\right)$[/tex]
D. [tex]$(3,12)$[/tex]
E. [tex]$(9,12)$[/tex]

Sagot :

GinnyAnswer
To determine the image of a vertex after dilation, you need to apply the scale factor to the coordinates of the original vertex. In this case, the scale factor is 3, and the original vertex is located at [tex]\((3, 4)\)[/tex].

Here’s the step-by-step process:

1. Identify the original coordinates: The original vertex is [tex]\((3, 4)\)[/tex].

2. Apply the scale factor: Multiply each coordinate of the original vertex by the scale factor.
- For the x-coordinate: [tex]\(3 \times 3 = 9\)[/tex]
- For the y-coordinate: [tex]\(4 \times 3 = 12\)[/tex]

3. Determine the new coordinates: The new coordinates after applying the scale factor are [tex]\((9, 12)\)[/tex].

Therefore, the image of the vertex located at [tex]\((3, 4)\)[/tex] after dilation with a scale factor of 3 is [tex]\((9, 12)\)[/tex].

The correct answer is [tex]\((9, 12)\)[/tex].
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