Questions: If ABCD is dilated by a factor of 1/2, the coordinate of C' would be:

Transcript text: If $A B C D$ is dilated by a factor of $\frac{1}{2}$, the coordinate of C' would be:

Solution

Solution Steps

To find the new coordinates of point $ C $ after dilation by a factor of $\frac{1}{2}$, we need to multiply the original coordinates of $ C $ by $\frac{1}{2}$.

Step 1: Understanding the Problem

We are given a point $ C $ which is part of a figure $ ABCD $. This figure is dilated by a factor of $ \frac{1}{2} $. We need to find the coordinates of the new point $ C' $ after the dilation.

Step 2: Dilation Formula

The dilation of a point $ (x, y) $ by a factor $ k $ with respect to the origin is given by: \[ (x', y') = (k \cdot x, k \cdot y) \] In this case, the dilation factor $ k $ is $ \frac{1}{2} $.

Step 3: Applying the Dilation

Let the coordinates of point $ C $ be $ (x_C, y_C) $. After dilation by a factor of $ \frac{1}{2} $, the coordinates of $ C' $ will be: \[ C' = \left( \frac{1}{2} \cdot x_C, \frac{1}{2} \cdot y_C \right) \]