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# Side lengths after dilation

Video transcript

The graph below contains
triangle ABC and the point P. Draw the image of triangle
ABC under a dilation whose center is P and a
scale factor of 2. So essentially, we
want to scale this so that every point is going
to be twice as far away from P. So for example,
B right over here has the same y-coordinate
as P, but its x-coordinate is three more. So we want to be twice as far. So if this maps to point B, we
just want to go twice as far. So we're at 3 away,
we want to go 6 away. So point P's x-coordinate
is at 3, now we're at 9. Likewise, point C
is 3 below P. Well we want to go twice as
far, so we'll go 3 more. And point A is 4 above P.
Well we want to go 4 more. We want to go twice as
far-- one, two, three, four. And we get right over there. Then they ask us,
what are the lengths of side AB and its image? AB right over
here, let's see, we might have to apply
the distance formula. Let's see, it's the
base right over here. The change in x between the two
is 3 and the change in y is 4, so this is actually a
3, 4, 5 right triangle. 3 squared plus 4 squared
is equal to 5 squared. So AB is 5 units long. Essentially just
using the Pythagorean theorem to figure that out. And its image, well it's
image should be twice as long. And let's see whether
that actually is the case. So this is a base right over
here that's of length 6. This has a height, or this
change in y, I could say. Because I'm really just trying
to figure out this length, which is the hypotenuse
of this right triangle. I don't have my drawing
tool, so I apologize. But this height right here is 8. So 8 squared is 64,
plus 6 squared is 36, that's 100, which is 10 squared. So notice, our scale factor
of 2, the corresponding side got twice as long. Each of these points
got twice as far away from our center of dilation.