If quadrilateral ABCD is dilated by a scale factor of 1.5, then what are the coordinates of point D ' ?

To find the coordinates of point D' after the dilation of quadrilateral ABCD by a scale factor of 1.5, follow these steps:

1. Break Down the Problem

We need to dilate point D's coordinates by the given scale factor.

2. Relevant Concepts

Dilation transforms points on a plane. If point $D$ has coordinates $(x, y)$, then the new coordinates $D'$ after dilation are calculated as: $D' = (kx, ky)$ where $k$ is the scale factor (1.5 in this case).

3. Analysis and Detail

Assuming the coordinates of point $D$ are given as $(x_D, y_D)$:

• The new x-coordinate will be $x' = 1.5 \times x_D$
• The new y-coordinate will be $y' = 1.5 \times y_D$

4. Verify and Summarize

To summarize, once you replace $x_D$ and $y_D$ with the actual coordinates of point $D$, you can compute the new coordinates $D'$ by applying the scale factor.

Final Answer

If the coordinates of point $D$ are $(x_D, y_D)$, then the coordinates of point $D'$ after dilation by a scale factor of 1.5 will be: $D' = \left(1.5 \times x_D, 1.5 \times y_D\right)$