Let ABC be the triangle where A is at (0, a), B is at (0, 0) and C is at (a, 0).
Note that BA = BC = a, as ABC is isosceles.
Also, ∠B = 90°
After a dilation with a scale factor of 1.8 with the origin as the center of dilation, length BA will be increased to 1.8 times and will become B'A'.
So, point A will be moved to (0, 1.8a).
Similarly, point C will be moved to (1.8a, 0).
Now, slope of A'C' = [tex]\frac{0-1.8a}{1.8a-0}[/tex]
= - 1.
Hence, the dilation preserves the slope of the hypotenuse.
