Math / Geometry

QuestionWhich transformation of $\triangle L M N$ produces the image $\triangle L^{\prime} M^{\prime} N^{\prime}$ ?
A reflection across the $y$ -axis, then a rotation $180^{\circ}$ clockwise.
A rotation $180^{\circ}$ clockwise, then a reflection over the $y$ -axis.
A translation of 1.5 units left, 0.5 unit up, then a reflection across the $x$ -axis.
A translation of 1.5 units left and 1.5 units down.

Studdy Solution

STEP 1

What is this asking? Which set of moves takes triangle $LMN$ and puts it in the position of triangle $L'M'N'$ ? Watch out! The order of transformations matters!
Flipping and then sliding is different than sliding and then flipping!

STEP 2

1. Analyze the change in L
2. Check if the same transformation works for M and N

STEP 3

Alright, let's focus on point $L$ first.
It starts at $(0, 2)$ and ends up at $(-3, -1.5)$ .
So, something funky is definitely happening!

STEP 4

Let's look at the x-coordinate.
It goes from $0$ to $-3$ .
That's a shift of $-3$ units.
In other words, $0 + (-3) = -3$ .

STEP 5

Now, the y-coordinate goes from $2$ to $-1.5$ .
That's a change of $-3.5$ units.
That is, $2 + (-3.5) = -1.5$ .

STEP 6

So, for $L$ , we have a shift of $(-3, -3.5)$ .
Let's see if this works for the other points!

STEP 7

Point $M$ starts at $(-2, 1)$ and moves to $(-5, -2.5)$ .

STEP 8

The x-coordinate changes by $-3$ because $-2 + (-3) = -5$ .
The y-coordinate changes by $-3.5$ because $1 + (-3.5) = -2.5$ .
Woohoo! Same change as $L$ !

STEP 9

Finally, point $N$ starts at $(1, 1)$ and lands at $(-2, -2.5)$ .

STEP 10

The x-coordinate changes by, you guessed it, $-3$ because $1 + (-3) = -2$ .
The y-coordinate also changes by $-3.5$ because $1 + (-3.5) = -2.5$ .
It's a match!

STEP 11

So, all three points move the exact same way: $3$ units left and $3.5$ units down.
That's a translation!

STEP 12

The correct transformation is a translation of $1.5$ units left and $1.5$ units down... oh wait!
That's not quite right.
It's actually a translation of $3$ units left and $3.5$ units down.
None of the provided options are correct!

Was this helpful?

Studdy Solution

STEP 1

What is this asking? Which set of moves takes triangle $LMN$ and puts it in the position of triangle $L'M'N'$ ? Watch out! The order of transformations matters!
Flipping and then sliding is different than sliding and then flipping!

STEP 2

1. Analyze the change in L
2. Check if the same transformation works for M and N

STEP 3

Alright, let's focus on point $L$ first.
It starts at $(0, 2)$ and ends up at $(-3, -1.5)$ .
So, something funky is definitely happening!

STEP 4

Let's look at the x-coordinate.
It goes from $0$ to $-3$ .
That's a shift of $-3$ units.
In other words, $0 + (-3) = -3$ .

STEP 5

Now, the y-coordinate goes from $2$ to $-1.5$ .
That's a change of $-3.5$ units.
That is, $2 + (-3.5) = -1.5$ .

STEP 6

So, for $L$ , we have a shift of $(-3, -3.5)$ .
Let's see if this works for the other points!

STEP 7

Point $M$ starts at $(-2, 1)$ and moves to $(-5, -2.5)$ .

STEP 8

The x-coordinate changes by $-3$ because $-2 + (-3) = -5$ .
The y-coordinate changes by $-3.5$ because $1 + (-3.5) = -2.5$ .
Woohoo! Same change as $L$ !

STEP 9

Finally, point $N$ starts at $(1, 1)$ and lands at $(-2, -2.5)$ .

STEP 10

The x-coordinate changes by, you guessed it, $-3$ because $1 + (-3) = -2$ .
The y-coordinate also changes by $-3.5$ because $1 + (-3.5) = -2.5$ .
It's a match!

STEP 11

So, all three points move the exact same way: $3$ units left and $3.5$ units down.
That's a translation!

STEP 12

The correct transformation is a translation of $1.5$ units left and $1.5$ units down... oh wait!
That's not quite right.
It's actually a translation of $3$ units left and $3.5$ units down.
None of the provided options are correct!

Get Studdy

Studdy solves anything!

Start learning now

Download Studdy AI Tutor now. Learn with ease and get all help you need to be successful at school.

Studdy Solution

STEP 1

What is this asking? Which set of moves takes triangle LMNLMNLMN and puts it in the position of triangle L′M′N′L'M'N'L′M′N′? Watch out! The order of transformations matters!Flipping and *then* sliding is different than sliding and *then* flipping!

STEP 2

1. Analyze the change in L2. Check if the same transformation works for M and N

STEP 3

Alright, let's **focus** on point LLL first.It starts at (0,2)(0, 2)(0,2) and ends up at (−3,−1.5)(-3, -1.5)(−3,−1.5).So, something funky is definitely happening!

STEP 4

Let's look at the *x*-coordinate.It goes from 000 to −3-3−3.That's a shift of −3-3−3 units.In other words, 0+(−3)=−30 + (-3) = -30+(−3)=−3.

STEP 5

Now, the *y*-coordinate goes from 222 to −1.5-1.5−1.5.That's a change of −3.5-3.5−3.5 units.That is, 2+(−3.5)=−1.52 + (-3.5) = -1.52+(−3.5)=−1.5.

STEP 6

So, for LLL, we have a shift of (−3,−3.5)(-3, -3.5)(−3,−3.5).Let's see if this works for the other points!

STEP 7

Point MMM starts at (−2,1)(-2, 1)(−2,1) and moves to (−5,−2.5)(-5, -2.5)(−5,−2.5).

STEP 8

The *x*-coordinate changes by −3-3−3 because −2+(−3)=−5-2 + (-3) = -5−2+(−3)=−5.The *y*-coordinate changes by −3.5-3.5−3.5 because 1+(−3.5)=−2.51 + (-3.5) = -2.51+(−3.5)=−2.5.Woohoo! Same change as LLL!

STEP 9

Finally, point NNN starts at (1,1)(1, 1)(1,1) and lands at (−2,−2.5)(-2, -2.5)(−2,−2.5).

STEP 10

The *x*-coordinate changes by, you guessed it, −3-3−3 because 1+(−3)=−21 + (-3) = -21+(−3)=−2.The *y*-coordinate also changes by −3.5-3.5−3.5 because 1+(−3.5)=−2.51 + (-3.5) = -2.51+(−3.5)=−2.5.It's a match!

STEP 11

So, all three points move the *exact same way*: 333 units left and 3.53.53.5 units down.That's a translation!

STEP 12

The correct transformation is a translation of 1.51.51.5 units left and 1.51.51.5 units down... oh wait!That's not quite right.It's actually a translation of 333 units left and 3.53.53.5 units down.None of the provided options are correct!

Get Studdy

Studdy solves anything!

Start learning now

Download Studdy AI Tutor now. Learn with ease and get all help you need to be successful at school.

What is this asking? Which set of moves takes triangle $LMN$ and puts it in the position of triangle $L'M'N'$ ? Watch out! The order of transformations matters!
Flipping and then sliding is different than sliding and then flipping!

1. Analyze the change in L
2. Check if the same transformation works for M and N

Alright, let's focus on point $L$ first.
It starts at $(0, 2)$ and ends up at $(-3, -1.5)$ .
So, something funky is definitely happening!

Let's look at the x-coordinate.
It goes from $0$ to $-3$ .
That's a shift of $-3$ units.
In other words, $0 + (-3) = -3$ .

Now, the y-coordinate goes from $2$ to $-1.5$ .
That's a change of $-3.5$ units.
That is, $2 + (-3.5) = -1.5$ .

So, for $L$ , we have a shift of $(-3, -3.5)$ .
Let's see if this works for the other points!

Point $M$ starts at $(-2, 1)$ and moves to $(-5, -2.5)$ .

The x-coordinate changes by $-3$ because $-2 + (-3) = -5$ .
The y-coordinate changes by $-3.5$ because $1 + (-3.5) = -2.5$ .
Woohoo! Same change as $L$ !

Finally, point $N$ starts at $(1, 1)$ and lands at $(-2, -2.5)$ .

The x-coordinate changes by, you guessed it, $-3$ because $1 + (-3) = -2$ .
The y-coordinate also changes by $-3.5$ because $1 + (-3.5) = -2.5$ .
It's a match!

So, all three points move the exact same way: $3$ units left and $3.5$ units down.
That's a translation!

The correct transformation is a translation of $1.5$ units left and $1.5$ units down... oh wait!
That's not quite right.
It's actually a translation of $3$ units left and $3.5$ units down.
None of the provided options are correct!