Question

in the standard (x, y) coordinate plane, a certain dilation maps the point (0,0) to itself and maps the point (4, - 10) to the point (1, - 4). (12, - 24) to the point

a. (3, - 6)
b. (9, - 36)
c. (15, - 36)
d. (10, - 20)

Explanation:

Step1: Find the scale factor

The scale factor \(k\) for dilation is found by dividing the coordinates of the image by the coordinates of the pre - image. For the \(x\) - coordinate: \(k=\frac{1}{4}\) (since the pre - image \(x\) - coordinate is \(4\) and the image \(x\) - coordinate is \(1\)).

Step2: Apply the scale factor to the new point

For the point \((12,-24)\), when we apply the dilation with scale factor \(k = \frac{1}{4}\):
The new \(x\) - coordinate is \(12\times\frac{1}{4}=3\).
The new \(y\) - coordinate is \(-24\times\frac{1}{4}=-6\).

Answer:

A. \((3, - 6)\)