Answer:
The scale factor of the dilation is 6.
Explanation:
Dilation of a Triangle
A dilation is a transformation that produces an image that is the same shape as the original but at a different size.
Dilating a point centered at the origin means multiplying its coordinates by a fixed scale factor k.
If point A(3,6) is dilated centered at the origin by a scale factor of 4, then its new coordinates are A'(12,24).
Triangle FGH has vertices F(−5, 0), G(0, 5), and H(5, 0).
It's known a dilation, centered at the origin, is applied to this triangle and the image has vertices F′(−30, 0), G′(0, 30), and H′(30, 0)
Comparing the coordinates F and F', the x-coordinate is scaled by a factor of (-30)/(-5)=6
Comparing the coordinates G and G', the y-coordinate is scaled by a factor of (30)/(5)=6
Comparing the coordinates H and H', the x-coordinate is scaled by a factor of (30)/(5)=6
Since all the scale factors are the same, we can conclude the scale factor of the dilation is 6.