Question

If triangle OPQ is dilated by a scale factor of two about the center of the triangle to create triangle O'P'Q', what can you conclude about segments RS and R'S'?

Segment O'Q' is perpendicular to segment R'S'.

Line RS is parallel to line R'S'.

Line RS is perpendicular to line R'S'.

Point P' passes through line RS.

Answer 1

Is that the entire question ?

Answer 2

Yes its with that picture i just sent ma'am.

Answer 3

Answer is easy, but justification is bit tricky...

Answer 4

Lets see, say :
coordinates of R = \(\large (x_1, y_1)\)
coordinates of S = \(\large (x_2, y_2)\)

Answer 5

I was thinking that they are paralell to one another

Answer 6

You're right !! they will be parallel.
you want to prove that ?

Answer 7

yes ma'am how do you prove that ,may you show me

Answer 8

sure :)
say the scale factor of dilation is \(\large k\),
can you find the image coordinates : R', S' ?

Answer 9

R' = ?
S' = ?

Answer 10

I dont get it

Answer 11

just multiply both x and y values by \(k\)

Answer 12

what number does k equal

Answer 13

coordinates of R' = \( \large (kx_1,k y_1)\)
coordinates of S' = \( \large (kx_2,k y_2)\)

Answer 14

Next we find the slopes of RS and R'S'

Answer 15

oh it would be r equal 1 and s equal 4

Answer 16

\(k\) is the scale factor - its just some number

Answer 17

` r equal 1 and s equal 4 `

wat do you mean ?

Answer 18

yes ma'am

Answer 19

the coordinates would be 1,4