Question

The image of ABC is A'B'C. What transformations would result in this image?

Answer 1

Answer:

ABC is reflected over the line $\displaystyle y = x - 1,$then T: $\displaystyle (x, y) → (x - 1, y - 1).$

Step-by-step explanation:

The line of $\displaystyle y = x - 1$is a slant graph, so reflecting the triangle over it will give us these coordinates so far:

$\displaystyle C[5, -4] → C'[-3, 4] \\ B[6, -3] → B'[-2, 5] \\ A[3, -2] → A'[-1, 2]$

Now, all you have left is the transformation rule of $\displaystyle [x - 1, y - 1].$This is what you end up with:

$\displaystyle C[-3, 4] → C'[-4, 3] \\ B[-2, 5] → B'[-3, 4] \\ A[-1, 2] → A'[-2, 1]$

And as you can see, this is a genuine statement!

I am joyous to assist you anytime.

* In case you do not know the linear graph of $\displaystyle y = x - 1,$look at the graph above.