Question

a. dilate each triangle using p as the center of dilation and the given scale factor.

1. scale factor: 2
2. scale factor: 1/2
3. scale factor: 3
4. scale factor: 1/3
5. scale factor: 4
6. scale factor: 1/4

Explanation:

Step1: Recall dilation rule

To dilate a triangle with center of dilation $P$ and scale - factor $k$, we multiply the distance between each vertex of the original triangle and the center of dilation $P$ by $k$ to get the new vertex.
For example, if a vertex $A$ of the original triangle has coordinates $(x_1,y_1)$ and the center of dilation $P$ has coordinates $(x_0,y_0)$, the coordinates of the dilated vertex $A'$ are given by $(x_0 + k(x_1 - x_0),y_0 + k(y_1 - y_0))$ in a coordinate - plane. In a non - coordinate geometric setting, we measure the distance from each vertex to $P$ and extend (if $k>1$) or contract (if $0 < k<1$) that distance by the factor $k$.

1. For scale factor $k = 2$:

• Measure the distance from each vertex of $\triangle ABC$ to $P$.
• Extend each of these distances by a factor of 2 to get the new vertices of the dilated triangle.

1. For scale factor $k=\frac{1}{2}$:

• Measure the distance from each vertex of $\triangle ABC$ to $P$.
• Contract each of these distances by a factor of $\frac{1}{2}$ to get the new vertices of the dilated triangle.

1. For scale factor $k = 3$:

• Measure the distance from each vertex of $\triangle ABC$ to $P$.
• Extend each of these distances by a factor of 3 to get the new vertices of the dilated triangle.

1. For scale factor $k=\frac{1}{3}$:

• Measure the distance from each vertex of $\triangle ABC$ to $P$.
• Contract each of these distances by a factor of $\frac{1}{3}$ to get the new vertices of the dilated triangle.

1. For scale factor $k = 4$:

• Measure the distance from each vertex of $\triangle ABC$ to $P$.
• Extend each of these distances by a factor of 4 to get the new vertices of the dilated triangle.

1. For scale factor $k=\frac{1}{4}$:

• Measure the distance from each vertex of $\triangle ABC$ to $P$.
• Contract each of these distances by a factor of $\frac{1}{4}$ to get the new vertices of the dilated triangle.

Since no specific coordinates or measurements are given, the general procedure for dilation is as described above.

Answer:

The dilated triangles are obtained by multiplying the distances from each vertex of the original triangle to the center of dilation $P$ by the given scale factor. For a scale factor $k>1$, the triangle is enlarged, and for $0 < k<1$, the triangle is reduced.