Question

If ABCD is dilated by a scale factor of 2 about point E, which of the following is true about line E prime F prime?

Square ABCD is shown with line EF running horizontally through the center of the figure.

line E prime F prime is perpendicular to line EF.
line E prime F prime is parallel to line EF.
line E prime F prime intersects with point B′.
line E prime F prime passes through the center of dilation.

Answer 1

what about this one

Answer 2

@az

Answer 3

For this question, you have to know dilation means.

Just like in your previous question- when we dilate a shape, you're keeping all the sides proportional and the angles will stay the same. The shape won't be rotating either

Answer 4

everything will stay the same?

Answer 5

The sides will get bigger or they could get smaller depending on our scale factor. In this case, it's 2 so the new figure will be bigger

Answer 6

im listening

Answer 7

But the sides still point in the same way so like

Answer 8

when you dilate, it's not going to change the way the shape is

Answer 9

do you see how the square got rotated

Answer 10

yes

Answer 11

that's a rotation AND a dilation

but this question, we only have a dilation

Answer 12

so it would pass through the center of dilation

Answer 13

So going back to your question, let's say this is our original image

Answer 14

What happens when you dilate the rectangle, won't we get something like this:

Answer 15

(not drawn perfectly but you should get the rough idea)

Answer 16

yes i get it

Answer 17

oh wait

Answer 18

what happen

Answer 19

We're dilating, yes, but we're doing it at point E so that means all the other points will become bigger but point E is fixed

Answer 20

what all would stay the same

Answer 21

Sorry I typed up something but it just would let me post it so I had to refresh the page

Answer 22

So what is the relationship between E'F' which is that new black line
and the old EF (in red)

are they parallel? perpendicular?
Does E'F' go through point B'?
or does it pass through the center of dilation

Answer 23

remember parallel lines do NOT intersect
perpendicular lines intersect at a 90 degree angle

Answer 24

it pass through the center of dilation

Answer 25

Bingo!

Answer 26

yessss

Answer 27

i have to more then im done