The dashed triangle is a dilation image of the solid triangle with the center at the origin. Is the dilation an enlargement or a reduction? Find the scale factor of the dilation.
The Solid Triangle has coordinates of: A(6,6)B(6,-6)C(-6,0)
The Dashed Triangle has coordinates of: A(2,1)B(2,-2)C(-2,0)
To determine if the dilation is an enlargement or a reduction, we can calculate the distance between the corresponding vertices of the solid and dashed triangles.
For triangle ABC:
AB = √[(6-6)^2 + (-6-6)^2] = √(0+72) = √72
BC = √[(-6+6)^2 + (0-(-6))^2] = √(0+36) = √36
AC = √[(6-(-6))^2 + (6-0)^2] = √(144+36) = √180 = 6√5
For triangle A'B'C':
A'B' = √[(2-2)^2 + (-2-1)^2] = √(0+9) = √9 = 3
B'C' = √[(-2+2)^2 + (0-(-2))^2] = √(0+4) = √4 = 2
A'C' = √[(2-(-2))^2 + (1-0)^2] = √(16+1) = √17
Now, we can see that the side lengths of the dashed triangle are smaller than the side lengths of the solid triangle. Therefore, the dilation is a reduction.
To find the scale factor of the dilation, we can calculate the ratio of the corresponding side lengths:
Scale factor = AB'/AB = 3/√72 = √72/72
Therefore, the scale factor of the dilation is √72/72.