Triangle PQR is transformed to triangle P′Q′R′. Triangle PQR has vertices P(4, 0), Q(0, −4), and R(−8, −4). Triangle P′Q′R′ has vertices P′(1, 0), Q′(0, −1), and R′(−2, −1).

Plot triangles PQR and P′Q′R′ on your own coordinate grid.

Part A: What is the scale factor of the dilation that transforms triangle PQR to triangle P′Q′R′? Explain your answer. (4 points)

Part B: Write the coordinates of triangle P′′Q′′R′′ obtained after P′Q′R′ is reflected about the y-axis. (4 points)

Part C: Are the two triangles PQR and P′'Q′'R′' congruent? Explain your answer. (2 points)

Question

Triangle PQR is transformed to triangle P′Q′R′. Triangle PQR has vertices P(4, 0), Q(0, −4), and R(−8, −4). Triangle P′Q′R′ has vertices P′(1, 0), Q′(0, −1), and R′(−2, −1).

Plot triangles PQR and P′Q′R′ on your own coordinate grid.

Part A: What is the scale factor of the dilation that transforms triangle PQR to triangle P′Q′R′? Explain your answer. (4 points)

Part B: Write the coordinates of triangle P′′Q′′R′′ obtained after P′Q′R′ is reflected about the y-axis. (4 points)

Part C: Are the two triangles PQR and P′'Q′'R′' congruent? Explain your answer. (2 points)

younggmoneyy · Answer

@darkknight

darkknight · Answer

have u plotted them yet?

younggmoneyy · Answer

yes

younggmoneyy · Answer

im stuck on part B

darkknight · Answer

alr if u already plotted the 2 triangles can u upload so i can get the visual? Easier for both of us so i don't have to plot again

darkknight · Answer

actually nvm i got it it won't tak elong

younggmoneyy · Answer

ok

darkknight · Answer

alr i plotted these. so Im going to assume you have P′Q′R' triangle plotted already? 
To reflect about the y-axis do you know what to do?

younggmoneyy · Answer

yes

darkknight · Answer

yes for the triangle being plotted or reflecting about y-axis?
Imagine i have a shape like this|dw:1608753952483:dw|
and I want to reflect about the y-axis
|dw:1608753975165:dw|
(That line I drew represents the y-axis)
So the reflective shape will look like this:
|dw:1608754013198:dw| (sort of not to scale)
Basically what happened is that all the y coordinates stayed the same, but the x coordinates are reflected, since the y-axis is x=0, then all the x coordinates are reflected by x=0, so if one of the original x coordinates was -2 it would be +2, if one was 5 the reflected about x=0 version would be -5

darkknight · Answer

So if you reflect  P′Q′R′ across the y-axis (x=0) all the y coordinates (the 3 y-coordinates) will stay the same and the x-coordinates will be negative to positive or positive to negative

younggmoneyy · Answer

ok, thank you, now I understand.

darkknight · Answer

No problem, need help on part 3?

younggmoneyy · Answer

sure.

darkknight · Answer

alr, so 2 triangles are always congruent if we apply transformations such as reflection, translation, and rotation. Think about it? If you turn a shape a few degrees it still has the congruency right? What about it you reflect it? still it does. If you move the shape it should still have congruency. Dilating a shape changes the size so no congruency if that happens. Based off of the transformations we did, what do you think?

darkknight · Answer

Key point, PQR and P′'Q′'R′' are these 2 triangles congruent? think about the transformations we did from PQR and P'Q'R' and from P'Q'R' to P''Q''R''

younggmoneyy · Answer

I think the 2 triangles are congruent because P"Q"R is just being reflected off of P'Q'R'. The shape dones't change.

darkknight · Answer

Im helping him lol, give me a min

darkknight · Answer

Almost correct.
Triangle PQR has vertices P(4, 0), Q(0, −4), and R(−8, −4). Triangle P′Q′R′ has vertices P′(1, 0), Q′(0, −1), and R′(−2, −1).
If you look at the original (THE original) triangle it is actually dilated by 4 times less, do you see that?

younggmoneyy · Answer

yes

darkknight · Answer

Okay, so  we have 1 dilation, u read this? 
$\color{#0cbb34}{\text{Originally Posted by}}$ darkknight
alr, so 2 triangles are always congruent if we apply transformations such as reflection, translation, and rotation. Think about it? If you turn a shape a few degrees it still has the congruency right? What about it you reflect it? still it does. If you move the shape it should still have congruency. Dilating a shape changes the size so no congruency if that happens. Based off of the transformations we did, what do you think?
$\color{#0cbb34}{\text{End of Quote}}$

younggmoneyy · Answer

yes

darkknight · Answer

ignore that user, so you think they are congruent now?

younggmoneyy · Answer

.... ummmm yes

darkknight · Answer

" Dilating a shape changes the size so no congruency if that happens..."
We dilated the shape from PQR to P'Q'R'
Therefore the shape is? congruent or not congruent?

darkknight · Answer

"two figures or objects are congruent if they have the same shape and size" dilating the shape changes the size

younggmoneyy · Answer

the shape is not congrunet

darkknight · Answer

Are the two triangles PQR and P′'Q′'R′' congruent?
You found them not to be. and I'll assume you know why they aren't?

younggmoneyy · Answer

yes, because the shape changed size and if it changes sizes then it's not congruent.

darkknight · Answer

Perfect, have a good day : )

younggmoneyy · Answer

thank you

jhonyy9 · Answer

good job @darkknight

darkknight · Answer

Thanks