Question

Create a scalene triangle ABC. Dilate the triangle with the center of dilation located outside of the triangle.

Answer 1

To create a dilated scalene triangle with an external center of dilation, draw a scalene triangle, select a point outside it as the center, connect the center to the vertices, choose a scale factor, and construct the dilated triangle using geometric construction.

Step-by-step explanation:

To create a scalene triangle ABC and perform dilation with the center outside the triangle, follow these steps:

1. Draw a scalene triangle ABC ensuring that all sides are of different lengths, indicating no two angles are the same.
2. Select a point outside of the triangle to be the center of dilation. Label it as point O.
3. Connect point O with each vertex of the triangle (points A, B, and C).
4. Choose a scale factor, k (k > 1 for an enlargement, 0 < k < 1 for a reduction).
5. Measure the lengths of segments OA, OB, and OC. Multiply each by the scale factor k to determine the lengths of the new segments.
6. From point O, draw new segments equal to the calculated lengths in the direction of the corresponding vertices. Label the endpoints of these new segments as A', B', and C'.
7. Connect points A', B', and C' to form the dilated scalene triangle A'B'C'.

The important aspect of geometric construction is to maintain the angles between the lines drawn from the center of dilation to the vertices of the triangle, thereby creating a similar triangle with sides proportional to the original based on the scale factor.