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ABC is an isosceles right triangle in which has a slope of -1 and mABC = 90°. ABC is dilated by a scale factor of 1.8 with the origin as the center of dilation, resulting in the image A'B'C'. What is the slope of ?
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First, we should look at dilation and what traits are retain and which change
A dilation is a transformation (notation ) that produces an image that is the same shape as the original, but is a different size. A dilation stretches or shrinks the original figure.
Properties preserved (invariant) under a dilation:
1. angle measures (remain the same)
2. parallelism (parallel lines remain parallel)
3. colinearity (points stay on the same lines)
4. midpoint (midpoints remain the same in each figure)
5. orientation (lettering order remains the same)
6. distance is NOT preserved (NOT an isometry)
(lengths of segments are NOT the same in all cases
except a scale factor or 1.)
Now your question is looking at the slope of A'C'
if your triangle goes from
           / |
          /  |
         /   |
 /|    /     |
/_|  /__ _|
Where A is bottom left corner, B is the right angle corner and C is top right corner
Property 1 states that your angles stay the same. So that would imply that AC and A'C' are parallel. Parallel lines will have the same slope. 
SO this means?
yes the slope of A'C' is the same as AC so it is -1