Question

If the figure shown on the grid below is dilated by a scale factor of 2/3 with the center of dilation at (-4,4), what is the coordinate of point M after the dilation?

Answer 1

What does it mean to dilate by a scale factor of 3?

The key thing is that the dilation value affects the distance between two points. As in the first example (dilation by a factor of 3), A is originally 1 unit down from P and 2 units to the left of P. 1*3 = 3, so A' (the dilated point) should be 3 unit

Explanation:

Answer 2

Explanation:

To determine the coordinate of point M after the dilation, we need to apply the scale factor and center of dilation to the original coordinates.

Given:

Scale factor = 2/3

Center of dilation = (-4, 4)

Let's assume the coordinates of point M in the original figure are (x, y). To find the new coordinates after dilation, we can use the following formula:

New x-coordinate = Center of dilation x-coordinate + (Original x-coordinate - Center of dilation x-coordinate) * Scale factor

New y-coordinate = Center of dilation y-coordinate + (Original y-coordinate - Center of dilation y-coordinate) * Scale factor

Substituting the given values, we have:

New x-coordinate = (-4) + (x - (-4)) * (2/3)

New y-coordinate = 4 + (y - 4) * (2/3)

Since we are specifically looking for the coordinate of point M after dilation, we can substitute M's original coordinates into the formulas. Let's assume the original coordinates of point M are (xM, yM):

New x-coordinate = (-4) + (xM - (-4)) * (2/3)

New y-coordinate = 4 + (yM - 4) * (2/3)

Now we have the coordinates of point M after the dilation.

Please provide the values of xM and yM to calculate the specific coordinate of point M after the dilation.