Question 1191529: Draw a triangle with vertices A(0, 4), B(2, -2), and C(-2, -2). Apply a dilation centered at the origin with scale factor to this triangle and draw the resulting triangle,A'B'C'. In complete sentences, describe the following:
The relationship between corresponding sides in terms of their lengths.
The relationship between corresponding sides in terms of their orientations.
The relationship between corresponding angles in terms of their measures.
Answer by CPhill(1959)   (Show Source):
You can put this solution on YOUR website! Here's a description of the dilation and the relationships between the original and dilated triangles:
**1. Drawing the Triangles:**
* **Triangle ABC:** Plot the points A(0, 4), B(2, -2), and C(-2, -2) on a coordinate plane and connect the points to form triangle ABC.
* **Dilation:** A dilation centered at the origin with a scale factor of 1/2 means that each point of the original triangle will be mapped to a new point that is half the distance from the origin. To find the coordinates of the dilated triangle A'B'C', multiply the coordinates of each vertex by 1/2:
* A'(0 * 1/2, 4 * 1/2) = A'(0, 2)
* B'(2 * 1/2, -2 * 1/2) = B'(1, -1)
* C'(-2 * 1/2, -2 * 1/2) = C'(-1, -1)
Plot these new points A'(0, 2), B'(1, -1), and C'(-1, -1) and connect them to form triangle A'B'C'. You'll notice that triangle A'B'C' is smaller than triangle ABC.
**2. Relationships between Corresponding Sides:**
* **Lengths:** The lengths of corresponding sides in the dilated triangle are *half* the lengths of the corresponding sides in the original triangle. For example, the length of A'B' is half the length of AB. This is because the scale factor of the dilation is 1/2.
* **Orientations:** The corresponding sides of the two triangles are *parallel* to each other. For example, side A'B' is parallel to side AB. The orientation of the sides is preserved in a dilation centered at the origin.
**3. Relationship between Corresponding Angles:**
The measures of corresponding angles in the two triangles are *equal*. For example, the measure of angle A is equal to the measure of angle A'. Dilations preserve angle measures.
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