The dashed triangle is a dilation image of the solid triangle. What is the scale factor?
mc048-1.jpg
2/π
To determine the scale factor between the solid triangle and the dashed triangle, we need to compare the corresponding side lengths of the two triangles.
1. Identify corresponding sides: Look for pairs of sides that are in the same position or have the same relative angle in both triangles. In this case, we can match the sides AC and A'B', BC and B'C', and AB and A'C' as corresponding sides.
2. Measure the lengths of the corresponding sides: Use a ruler or measuring tool to determine the lengths of each of the corresponding sides. In this case, let's assume that AC has a length of 6 units in the solid triangle and A'B' has a length of 3 units in the dashed triangle. Similarly, let's say BC has a length of 8 units in the solid triangle and B'C' has a length of 4 units in the dashed triangle.
3. Calculate the scale factor: The scale factor is the ratio between the lengths of the corresponding sides in the two triangles. To find the scale factor, divide the length of the corresponding side in the dashed triangle by the length of the corresponding side in the solid triangle.
Let's calculate the scale factor for side AC and A'B':
Scale factor = Length of A'B' / Length of AC
= 3 units / 6 units
= 0.5
Similarly, the scale factor for side BC and B'C' would also be 0.5.
Therefore, the scale factor between the solid triangle and the dashed triangle is 0.5.