Question

triangle ABC has vertices point A (2,1) point B (-2,2) and point C (-3,-1) after dilation triangle A'B'C has vertices point A' (4,2) point B'(-4,4) and point C' (-6,-2) determine the scale factor for the dilation of triangle ABC with a center point of dilation at the origin (0,0)

Answer 1

[AI-generated answer — Bot GPT 3.5]

To find the scale factor of the dilation, we can use the distance formula between the corresponding vertices of the two triangles.

For points A and A', we have:

sqrt((4-0)^2 + (2-0)^2) = sqrt(16 + 4) = sqrt(20) = 2sqrt(5)

Similarly, for points B and B', we have:

sqrt((-4-0)^2 + (4-0)^2) = sqrt(16 + 16) = 4

And for points C and C', we have:

sqrt((-6-0)^2 + (-2-0)^2) = sqrt(36 + 4) = sqrt(40) = 2sqrt(10)

The scale factor of the dilation is the ratio of the corresponding side lengths:

Scale factor = Corresponding side length in the image / Corresponding side length in the pre-image

So, the scale factor for the dilation of triangle ABC with a center point at the origin is:

2sqrt(5) / 2 = sqrt(5)

Therefore, the scale factor of the dilation is sqrt(5).