Describe the single transformation that would map triangle 𝐴𝐵𝐶 onto triangle 𝐴 prime 𝐵 prime 𝐶 prime in the given figure.
Triangle 𝐴𝐵𝐶 is found here. Triangle 𝐴 prime 𝐵 prime 𝐶 prime is found here. So triangle 𝐴𝐵𝐶 was moved onto triangle 𝐴 prime 𝐵 prime 𝐶 prime. This was the new spot. This is where it was. We’ll say old. And this is where it is now. So we’ll say new.
So to decide that, let’s look at the points. How would we have got in from 𝐴 to 𝐴 prime? Well, we can simply count how many spaces will we have to move: one, two, three, four, five, six, seven, so seven units right and one, two units down. Now, this should be uniform throughout the whole triangle.
So to get from 𝐵 to 𝐵 prime, we should have to do the exact same thing, seven units right and two units down. And now, let’s check 𝐶 to 𝐶 prime, seven units right and two down.
So this will be our single transformation. And moving like this is called a translation. It’s like sliding. The triangle wasn’t flipped upside down or rotated. It was simply just shifted.
Therefore, our final answer will be a translation seven right and two down.