Dilate the point P(-6,-4) by a scale factor of 0.5, about the origin. Where is P' located?


To dilate a point by a scale factor about the origin, we multiply each coordinate of the point by the scale factor.

Given point \( P(-6, -4) \) and the scale factor \( 0.5 \), the coordinates of the dilated point \( P' \) are calculated as:

\[
P' = (x', y') = (0.5 \cdot (-6), 0.5 \cdot (-4))
\]

\[
P' = (-3, -2)
\]

Thus, the point \( P' \) after dilation is located at \( (-3, -2) \).

Would you like any further details or have any questions?

Here are 5 related questions:
1. How would the coordinates change if the scale factor were 2 instead of 0.5?
2. What happens to the coordinates of a point if the dilation is centered at a different point than the origin?
3. How do you dilate a point if the center of dilation is at \( (2, -1) \)?
4. How does dilation differ from translation in terms of how points move on the plane?
5. What would the new coordinates of \( P \) be if the scale factor was negative?

**Tip:** Dilation preserves the shape but changes the size of geometric figures based on the scale factor.

Dilate the point P(-6,-4) by a scale factor of 0.5, about the origin. Where is P' located?

Learn how to dilate the point P(-6,-4) by a scale factor of 0.5 about the origin. This problem demonstrates how to apply dilation transformations in geometry, including the use of the dilation theorem and related formulas. Suitable for students in Grades 8-10.

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