# Question Video: Identifying the Types of Transformations Applied on a Given Figure from the Graph Mathematics • 8th Grade

In the given figure, what combination of transformations would map circle 𝐴 onto circle 𝐵?

03:05

### Video Transcript

In the given figure, what combination of transformations would map circle 𝐴 onto circle 𝐵? Is it (A) a translation of two right and six down followed by a dilation of scale factor two? (B) A translation of two left and six up followed by a dilation of scale factor two. (C) A translation of four left and two down followed by a dilation of scale factor one. (D) A translation of six left and two up followed by a dilation of scale factor one. Or is it (E) a translation of six right and two down followed by a dilation of scale factor two?

So, we’re looking for a combination of transformations. So, that tells us we’re going to be describing more than one. And we’re mapping circle 𝐴, that’s the circle with center at negative three, three, onto circle 𝐵, that’s the larger circle with center at three, one.

Let’s remind ourselves the four transformations we tend to use. They are reflections, rotations, dilations, and translations. The “fl” in the word reflection remind us that when we reflect a shape, we flip it over a mirror line. When we rotate a shape, we “t” turn it about a center in a given direction and angle. When we dilate a shape, which is sometimes called enlarging it, we make it either larger or smaller. And finally, when we translate a shape, we slide it.

So, let’s look at what we’ve done to map circle 𝐴 onto circle 𝐵. And we’re going to use the center as the point of reference. Firstly, we see that to map circle 𝐴 onto circle 𝐵, we need to move the entire circle right a number of units. In fact, we need to move it right six units. We then move it down two units. And so, we can see that we’re actually beginning with a slide. We’re beginning with a translation six units right and two units down.

But then what happens? We said earlier that circle 𝐵 is much larger than circle 𝐴. And so we must be dilating or enlarging the circle. When we enlarge or dilate a shape, we describe it in terms of its scale factor. And the scale factor is calculated by dividing a length on the new shape by the corresponding length on the old shape. So, in this case, let’s look at the radii of our circles.

The radius is a line joining the center to a point on the circumference. So we can actually choose any point here. On our larger circle, the radius is two units in length. And on our smaller original circle, the radius is one unit. So, the scale factor for enlargement or dilation here must be two divided by one, which is simply two.

And so, we see that we have a translation six units right and two units down followed by a dilation with a scale factor of two. Let’s compare this to the options given in our question. When we do, we see that the correct answer is (E). It’s a translation of six right and two down followed by a dilation of scale factor two.