Question

3. Use rigid motions to explain whether the triangles in the figure are congruent. Be sure to describe specific rigid motions in your explanation.

Answer 1

@dumbcow

Answer 2

@retirEEd @zepdrix plz help

Answer 3

@Will.H

Answer 4

Here's a definition of rigid motion.
http://www.math.washington.edu/~julia/simuw_07/Ex1_isom.pdf
all of the mention transformation you would certainly be familiar with.
It is not sure which of the figures is the preimage and which one is the image.
For the purpose of discussion, you can assume any one.
Do you see which kind of rigid motion is shown in the figure?

Answer 5

it looks like it rotated counterclockwise, the center being (1, -1)

Answer 6

looks like a rotation clockwise with a glide reflection... idk

Answer 7

Rigid motion applies for many kinds of transportations such as rotation and translation I bet we can have both in here.
The triangle PDW can shift to the position of triangle SMJ
We have a counterclockwise rotation of 90 degree and a translation of 2 units down
Proof:
Rotation 90 degrees counterclockwise of point D(-2,4) it's corresponding point is M(-4,-4) Let's see if we will get same result when we apply rotation and translation
So rotation 90 degrees counterclockwise D(-2,4) --> (-4,-2)
Translation 2 units down
(-4,-2)--> (-4,-4) works so therefore they are congruent with rigid motion rotation and translation

Answer 8

Autocorrect made it transportation instead of the word transformations.. XD

Answer 9

I have a question.......like which triangle was moved all the points are different and the question doesnt tell you which is the original

Answer 10

Indeed but we can make an assumption to prove the point

Answer 11

so the anwser is counterclockwise turn 90 degrees and a translation of 2 units up

Answer 12

If we can have one figure map the other then we can determine they are congruent

Answer 13

2 units down not up

Answer 14

And give a brief explanation

Answer 15

ok

Answer 16

Thanks will... appreciate it

Answer 17

@Devonhoward15
If you have already done rotation about a point other than the origin, then an alternative answer is possible, namely that suggested by @OtherWorldly, which is a counterclockwise rotation of 90 degrees about (1,-1) from PDW to SMJ. In that case no translation is needed. In fact, all rotations can be done without translation if we find the appropriate centre of rotation.

Answer 18

How can the center be 1,-1! It can be other than the origin but it must be at least one of the figures points

Answer 19

I'd suggest to stick with the origin because it is most suitable

Answer 20

Since the figure is closely laying on it

Answer 21

ok but hat just complicates the answer

Answer 22

that*

Answer 23

Actually rotation about (1,-1) is a simpler \(answer\), because it involves only one operation. However, it may not be familiar to everyone how the centre of rotation can be found. So it may appear \(finding\) the solution is more complicated.

Answer 24

Yeah well there are plenty of ways to solve a question

Answer 25

C ya guys

Answer 26

Exactly, I am just giving credit to the first proposed correct solution, and is proposed as an alternative.

Answer 27

Fair enough

Answer 28

DPW rotates counterclockwise making the coordinates go from D( -2, 4) to (-2, -4), W( -1, 2) to ( -1, -2), and P( 3, 3) to ( -3, 3). move all the coordinates -1 on the y axis and -2 on the x axis ( -1, -2) to align it with MSJ @Will.H

Answer 29

@OtherWorldly
I think @Will.H knows how to do the transformation. lol
To find the centre of rotation, we only need to join the corresponding points (like DM,PS,WJ) and draw perpendicular bisectors to these segments. The point where the perp. bisectors meet is the centre of rotation.