Myles was asked to draw a triangle xyz and then dilate it using the origin aa the center of dilation and a scale factor of 0.75.he thinks adding 0.75 units to the coordinates of the vertices of xyz will help him draw the dilated image. Explain why miles is incorrect,and what he needs to do to graph the dilation.

it's a dilation, not a translation.

for a dilation, each coordinate is multiplied by the scale factor.

Myles is incorrect in thinking that adding 0.75 units to the coordinates of the vertices of triangle XYZ will help him draw the dilated image. Here's why:

To dilate a shape, we need to adjust the distance of each point from the center of dilation according to the given scale factor. The scale factor determines how much the shape will be expanded or contracted.

In this case, the center of dilation is the origin (0,0), and the scale factor is 0.75. To dilate a point, we multiply its coordinates by the scale factor.

To graph the dilation of triangle XYZ, Myles should follow these steps:

1. Find the coordinates of each vertex of triangle XYZ.
2. Multiply the coordinates of each vertex by the scale factor of 0.75.
For example, if the original coordinates of vertex X are (x1, y1), the dilated coordinates will be (0.75 * x1, 0.75 * y1). Repeat this for each vertex.
3. Plot the dilated coordinates to graph the dilated image of triangle XYZ.

By following these steps, Myles will accurately graph the dilated image of triangle XYZ with the origin as the center of dilation and a scale factor of 0.75.

Myles is incorrect in thinking that adding 0.75 units to the coordinates of the vertices of XYZ will accurately draw the dilated image. The reason is that a dilation with a scale factor of 0.75 involves shrinking the original image. Adding a value to the coordinates would actually result in expanding the image, not shrinking it.

To correctly graph the dilated image, Myles needs to follow these steps:

1. Draw the original triangle XYZ.
2. Identify the center of dilation, which in this case is the origin (0,0).
3. Determine the scale factor, which is given as 0.75.
4. For each vertex of the original triangle, perform the following steps:
- Multiply the x-coordinate of the vertex by the scale factor.
- Multiply the y-coordinate of the vertex by the scale factor.
- This will give you the corresponding coordinates for the dilated image.
5. Connect the new coordinates to form the dilated triangle.

By multiplying the coordinates of each vertex by the scale factor, Myles can properly "shrink" the original triangle XYZ around the origin, resulting in the correct dilated image.