Math / Geometry

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The figure below is dilated by a factor of 3 centered at the origin. Plot the resulting image.
Click twice to plot a segment. Click a segment to delete it.

Studdy Solution

STEP 1

What is this asking? We need to make a bigger version of the shape, three times bigger, by stretching it out from the center of the graph. Watch out! Don't just add 3 to each coordinate!
We need to multiply by the scale factor, which is 3.

STEP 2

1. Dilate Point P
2. Dilate Point Q
3. Dilate Point R
4. Dilate Point N

STEP 3

Alright, let's start with point P!
Its current coordinates are $(3, 1)$ .
We're dilating by a factor of 3 centered at the origin.
This means we multiply each coordinate by our scale factor of 3.

STEP 4

So, the new x-coordinate of P, let's call it P', will be $3 \cdot 3 = 9$ .
And the new y-coordinate will be $3 \cdot 1 = 3$ .
That gives us P' at $(9, 3)$ .
Boom!

STEP 5

Next up is point Q, currently at $(-2, 3)$ .
Remember, we multiply each coordinate by our scale factor of 3.

STEP 6

The new x-coordinate of Q' will be $3 \cdot (-2) = -6$ .
The new y-coordinate will be $3 \cdot 3 = 9$ .
So, Q' lands at $(-6, 9)$ .
Fantastic!

STEP 7

Now for point R, starting at $(-3, 0)$ .
We're still multiplying by 3.

STEP 8

The new x-coordinate of R' is $3 \cdot (-3) = -9$ .
The new y-coordinate is $3 \cdot 0 = 0$ .
R' is chilling at $(-9, 0)$ .
Nice!

STEP 9

Finally, let's tackle point N, currently at $(1, -2)$ .
We're multiplying by our scale factor of 3.

STEP 10

The new x-coordinate of N' is $3 \cdot 1 = 3$ .
The new y-coordinate is $3 \cdot (-2) = -6$ .
So, N' is hanging out at $(3, -6)$ .
Perfect!

STEP 11

The new dilated quadrilateral is formed by the points P' $(9, 3)$ , Q' $(-6, 9)$ , R' $(-9, 0)$ , and N' $(3, -6)$ .
Plot these points on the graph, connect the dots, and you've got your dilated image!

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Questionng.com Google Chrome We... Dashboard NCcloud YouTube TikTok - Make Your... Login Other favorite
The figure below is dilated by a factor of 3 centered at the origin. Plot the resulting image.
Click twice to plot a segment. Click a segment to delete it.

Studdy Solution

STEP 1

What is this asking? We need to make a bigger version of the shape, three times bigger, by stretching it out from the center of the graph. Watch out! Don't just add 3 to each coordinate!
We need to multiply by the scale factor, which is 3.

STEP 2

1. Dilate Point P
2. Dilate Point Q
3. Dilate Point R
4. Dilate Point N

STEP 3

Alright, let's start with point P!
Its current coordinates are $(3, 1)$ .
We're dilating by a factor of 3 centered at the origin.
This means we multiply each coordinate by our scale factor of 3.

STEP 4

So, the new x-coordinate of P, let's call it P', will be $3 \cdot 3 = 9$ .
And the new y-coordinate will be $3 \cdot 1 = 3$ .
That gives us P' at $(9, 3)$ .
Boom!

STEP 5

Next up is point Q, currently at $(-2, 3)$ .
Remember, we multiply each coordinate by our scale factor of 3.

STEP 6

The new x-coordinate of Q' will be $3 \cdot (-2) = -6$ .
The new y-coordinate will be $3 \cdot 3 = 9$ .
So, Q' lands at $(-6, 9)$ .
Fantastic!

STEP 7

Now for point R, starting at $(-3, 0)$ .
We're still multiplying by 3.

STEP 8

The new x-coordinate of R' is $3 \cdot (-3) = -9$ .
The new y-coordinate is $3 \cdot 0 = 0$ .
R' is chilling at $(-9, 0)$ .
Nice!

STEP 9

Finally, let's tackle point N, currently at $(1, -2)$ .
We're multiplying by our scale factor of 3.

STEP 10

The new x-coordinate of N' is $3 \cdot 1 = 3$ .
The new y-coordinate is $3 \cdot (-2) = -6$ .
So, N' is hanging out at $(3, -6)$ .
Perfect!

STEP 11

The new dilated quadrilateral is formed by the points P' $(9, 3)$ , Q' $(-6, 9)$ , R' $(-9, 0)$ , and N' $(3, -6)$ .
Plot these points on the graph, connect the dots, and you've got your dilated image!

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Questionng.com Google Chrome We... Dashboard NCcloud YouTube TikTok - Make Your... Login Other favoriteThe figure below is dilated by a factor of 3 centered at the origin. Plot the resulting image.Click twice to plot a segment. Click a segment to delete it.

Studdy Solution

STEP 1

What is this asking? We need to make a bigger version of the shape, **three times** bigger, by stretching it out from the center of the graph. Watch out! Don't just add 3 to each coordinate!We need to *multiply* by the **scale factor**, which is **3**.

STEP 2

1. Dilate Point P2. Dilate Point Q3. Dilate Point R4. Dilate Point N

STEP 3

Alright, let's **start with point P**!Its current coordinates are (3,1) (3, 1) (3,1).We're dilating by a factor of **3** centered at the origin.This means we **multiply** each coordinate by our **scale factor** of **3**.

STEP 4

So, the new x-coordinate of P, let's call it P', will be 3⋅3=9 3 \cdot 3 = 9 3⋅3=9.And the new y-coordinate will be 3⋅1=3 3 \cdot 1 = 3 3⋅1=3.That gives us P' at (9,3) (9, 3) (9,3).Boom!

STEP 5

Next up is **point Q**, currently at (−2,3) (-2, 3) (−2,3).Remember, we **multiply** each coordinate by our **scale factor** of **3**.

STEP 6

The new x-coordinate of Q' will be 3⋅(−2)=−6 3 \cdot (-2) = -6 3⋅(−2)=−6.The new y-coordinate will be 3⋅3=9 3 \cdot 3 = 9 3⋅3=9.So, Q' lands at (−6,9) (-6, 9) (−6,9).Fantastic!

STEP 7

Now for **point R**, starting at (−3,0) (-3, 0) (−3,0).We're still **multiplying** by **3**.

STEP 8

The new x-coordinate of R' is 3⋅(−3)=−9 3 \cdot (-3) = -9 3⋅(−3)=−9.The new y-coordinate is 3⋅0=0 3 \cdot 0 = 0 3⋅0=0.R' is chilling at (−9,0) (-9, 0) (−9,0).Nice!

STEP 9

Finally, let's tackle **point N**, currently at (1,−2) (1, -2) (1,−2).We're **multiplying** by our **scale factor** of **3**.

STEP 10

The new x-coordinate of N' is 3⋅1=3 3 \cdot 1 = 3 3⋅1=3.The new y-coordinate is 3⋅(−2)=−6 3 \cdot (-2) = -6 3⋅(−2)=−6.So, N' is hanging out at (3,−6) (3, -6) (3,−6).Perfect!

STEP 11

The new dilated quadrilateral is formed by the points P'(9,3)(9, 3)(9,3), Q'(−6,9)(-6, 9)(−6,9), R'(−9,0)(-9, 0)(−9,0), and N'(3,−6)(3, -6)(3,−6).Plot these points on the graph, connect the dots, and you've got your dilated image!

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Start learning now

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

Questionng.com Google Chrome We... Dashboard NCcloud YouTube TikTok - Make Your... Login Other favorite
The figure below is dilated by a factor of 3 centered at the origin. Plot the resulting image.
Click twice to plot a segment. Click a segment to delete it.

What is this asking? We need to make a bigger version of the shape, three times bigger, by stretching it out from the center of the graph. Watch out! Don't just add 3 to each coordinate!
We need to multiply by the scale factor, which is 3.

1. Dilate Point P
2. Dilate Point Q
3. Dilate Point R
4. Dilate Point N

Alright, let's start with point P!
Its current coordinates are $(3, 1)$ .
We're dilating by a factor of 3 centered at the origin.
This means we multiply each coordinate by our scale factor of 3.

So, the new x-coordinate of P, let's call it P', will be $3 \cdot 3 = 9$ .
And the new y-coordinate will be $3 \cdot 1 = 3$ .
That gives us P' at $(9, 3)$ .
Boom!

Next up is point Q, currently at $(-2, 3)$ .
Remember, we multiply each coordinate by our scale factor of 3.

The new x-coordinate of Q' will be $3 \cdot (-2) = -6$ .
The new y-coordinate will be $3 \cdot 3 = 9$ .
So, Q' lands at $(-6, 9)$ .
Fantastic!

Now for point R, starting at $(-3, 0)$ .
We're still multiplying by 3.

The new x-coordinate of R' is $3 \cdot (-3) = -9$ .
The new y-coordinate is $3 \cdot 0 = 0$ .
R' is chilling at $(-9, 0)$ .
Nice!

Finally, let's tackle point N, currently at $(1, -2)$ .
We're multiplying by our scale factor of 3.

The new x-coordinate of N' is $3 \cdot 1 = 3$ .
The new y-coordinate is $3 \cdot (-2) = -6$ .
So, N' is hanging out at $(3, -6)$ .
Perfect!

The new dilated quadrilateral is formed by the points P' $(9, 3)$ , Q' $(-6, 9)$ , R' $(-9, 0)$ , and N' $(3, -6)$ .
Plot these points on the graph, connect the dots, and you've got your dilated image!