QuestionIdentify the transformation for $\triangle XYZ$ from $\triangle ABC$ and describe the rule for transforming $D(0,3)$ to $D'(3,0)$ .

Studdy Solution

STEP 1

Assumptions1. The vertices of the original triangle are D(0,3),(1,8), and F(-3,4). . The vertices of the transformed triangle are D'(3,0),'(8,-1), and F'(4,3).
3. The transformation involves only one type of transformation (either translation, reflection, or rotation).

STEP 2

First, let's compare the coordinates of the original triangle and the transformed triangle. $(0,) \rightarrow D'(,0)$ $(1,8) \rightarrow'(8,-1)$ $(-,4) \rightarrow F'(4,)$

STEP 3

We can see that in each pair, the x and y coordinates have been swapped. This indicates a reflection over the line y=x.

STEP 4

To confirm this, we can write the rule for a reflection over the line y=x. For any point (x, y), the reflected point is (y, x).

STEP 5

Now, let's apply this rule to the vertices of the original triangle and see if we get the vertices of the transformed triangle.
$(0,3) \rightarrow D'(3,0)$ $(1,8) \rightarrow'(8,1)$ $(-3,4) \rightarrow F'(4,-3)$

STEP 6

We can see that the rule doesn't give us the correct transformed points. This means that there is another transformation involved.

STEP 7

Let's try adding a reflection over the x-axis to our transformation. The rule for a reflection over the x-axis is (x, y) -> (x, -y).

STEP 8

Now, let's apply this rule to the points we got from the reflection over the line y=x.
$'(3,0) \rightarrow D''(3,0)$ $'(8,1) \rightarrow''(8,-1)$ $'(4,-3) \rightarrow F''(4,3)$

STEP 9

Now we can see that applying both transformations gives us the correct transformed points. So the transformation used to create triangle D'E'' from triangle DEF is a reflection over the line y=x followed by a reflection over the x-axis.
The rule for this transformation is (x, y) -> (y, -x).

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QuestionIdentify the transformation for $\triangle XYZ$ from $\triangle ABC$ and describe the rule for transforming $D(0,3)$ to $D'(3,0)$ .

Studdy Solution

STEP 1

Assumptions1. The vertices of the original triangle are D(0,3),(1,8), and F(-3,4). . The vertices of the transformed triangle are D'(3,0),'(8,-1), and F'(4,3).
3. The transformation involves only one type of transformation (either translation, reflection, or rotation).

STEP 2

First, let's compare the coordinates of the original triangle and the transformed triangle. $(0,) \rightarrow D'(,0)$ $(1,8) \rightarrow'(8,-1)$ $(-,4) \rightarrow F'(4,)$

STEP 3

We can see that in each pair, the x and y coordinates have been swapped. This indicates a reflection over the line y=x.

STEP 4

To confirm this, we can write the rule for a reflection over the line y=x. For any point (x, y), the reflected point is (y, x).

STEP 5

Now, let's apply this rule to the vertices of the original triangle and see if we get the vertices of the transformed triangle.
$(0,3) \rightarrow D'(3,0)$ $(1,8) \rightarrow'(8,1)$ $(-3,4) \rightarrow F'(4,-3)$

STEP 6

We can see that the rule doesn't give us the correct transformed points. This means that there is another transformation involved.

STEP 7

Let's try adding a reflection over the x-axis to our transformation. The rule for a reflection over the x-axis is (x, y) -> (x, -y).

STEP 8

Now, let's apply this rule to the points we got from the reflection over the line y=x.
$'(3,0) \rightarrow D''(3,0)$ $'(8,1) \rightarrow''(8,-1)$ $'(4,-3) \rightarrow F''(4,3)$

STEP 9

Now we can see that applying both transformations gives us the correct transformed points. So the transformation used to create triangle D'E'' from triangle DEF is a reflection over the line y=x followed by a reflection over the x-axis.
The rule for this transformation is (x, y) -> (y, -x).

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QuestionIdentify the transformation for △XYZ\triangle XYZ△XYZ from △ABC\triangle ABC△ABC and describe the rule for transforming D(0,3)D(0,3)D(0,3) to D′(3,0)D'(3,0)D′(3,0).

Studdy Solution

STEP 1

Assumptions1. The vertices of the original triangle are D(0,3),(1,8), and F(-3,4). . The vertices of the transformed triangle are D'(3,0),'(8,-1), and F'(4,3).3. The transformation involves only one type of transformation (either translation, reflection, or rotation).

STEP 2

First, let's compare the coordinates of the original triangle and the transformed triangle.(0,)→D′(,0)(0,) \rightarrow D'(,0)(0,)→D′(,0)(1,8)→′(8,−1)(1,8) \rightarrow'(8,-1)(1,8)→′(8,−1)(−,4)→F′(4,)(-,4) \rightarrow F'(4,)(−,4)→F′(4,)

STEP 3

We can see that in each pair, the x and y coordinates have been swapped. This indicates a reflection over the line y=x.

STEP 4

To confirm this, we can write the rule for a reflection over the line y=x. For any point (x, y), the reflected point is (y, x).

STEP 5

STEP 6

We can see that the rule doesn't give us the correct transformed points. This means that there is another transformation involved.

STEP 7

Let's try adding a reflection over the x-axis to our transformation. The rule for a reflection over the x-axis is (x, y) -> (x, -y).

STEP 8

STEP 9

Now we can see that applying both transformations gives us the correct transformed points. So the transformation used to create triangle D'E'' from triangle DEF is a reflection over the line y=x followed by a reflection over the x-axis.The rule for this transformation is (x, y) -> (y, -x).

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.

QuestionIdentify the transformation for $\triangle XYZ$ from $\triangle ABC$ and describe the rule for transforming $D(0,3)$ to $D'(3,0)$ .

Assumptions1. The vertices of the original triangle are D(0,3),(1,8), and F(-3,4). . The vertices of the transformed triangle are D'(3,0),'(8,-1), and F'(4,3).
3. The transformation involves only one type of transformation (either translation, reflection, or rotation).

First, let's compare the coordinates of the original triangle and the transformed triangle. $(0,) \rightarrow D'(,0)$ $(1,8) \rightarrow'(8,-1)$ $(-,4) \rightarrow F'(4,)$

Now we can see that applying both transformations gives us the correct transformed points. So the transformation used to create triangle D'E'' from triangle DEF is a reflection over the line y=x followed by a reflection over the x-axis.
The rule for this transformation is (x, y) -> (y, -x).