Question

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 ?

A. - 1
B. 0
C. 1
D. 1.5
E. 2

Answer 1

-1

Explanation:

Answer 2

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' =
`(0-1.8a)/(1.8a-0)`

= - 1.

Hence, the dilation preserves the slope of the hypotenuse.