Question

A segment with endpoints (3, –2) and (4, 2) is dilated to the image segment with endpoints (9, –6) and (12, 6). What is the scale factor for the dilation?

Answer 1

Find the magnitude of both lines, then find the constant value multiplied by the magnitude of line 1, which will result in magnitude of length 2.

Answer 2

we have a factor of 3 here, I'll explain with a drawing

Answer 3

\[\sqrt{(4-3)^2+(2-(-2))^2}\times x = \sqrt{(12-9)^2+(6-(-6))^2}\]
\[\sqrt{17} \times x = \sqrt{9 + 144}\]
\[\sqrt{17} \times x = \sqrt{153}\]
\[x = \frac{\sqrt{153}}{\sqrt{17}} = \sqrt{\frac{153}{17}} = \sqrt{9} = 3\]

Answer 4

the hiding number above on the right is 12
so 12/4 = 3
and 3/1 = 3
these are the sides of the formed triangles