Triangle FGH has vertices F(−5, 0), G(0, 5), and H(5, 0). A dilation, centered at the origin, is applied to this triangle. The image has vertices F′(−30, 0), G′(0, 30), and H′(30, 0). What is the scale factor of this dilation?

The scale factor of the dilation is 6.

Step-by-step 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.