QuestionFind the reflection rule for triangle $C(3,8), D(5,12), E(4,6)$ to $C'(-8,-3), D'(-12,5), E'(-6,-4)$ .

Studdy Solution

STEP 1

Assumptions1. The coordinates of the original triangle are C(3,8), D(5,12),(4,6) . The coordinates of the reflected image are C'(-8,-3), D'(-12,5),'(-6,-4)

STEP 2

We can start by comparing the coordinates of the original points and their reflected images. This will help us determine the rule of reflection.

STEP 3

Let's compare the coordinates of point C and its reflected image C'. $C(3,8) \rightarrow C'(-8,-3)$

STEP 4

We can see that the x-coordinate and y-coordinate of point C have been negated to obtain the coordinates of point C'. This suggests that the reflection might be over the origin.

STEP 5

To confirm this, let's compare the coordinates of point D and its reflected image D'. $(5,12) \rightarrow D'(-12,5)$

STEP 6

Again, we can see that the x-coordinate and y-coordinate of point D have been negated to obtain the coordinates of point D'. This further supports the idea that the reflection might be over the origin.

STEP 7

Finally, let's compare the coordinates of point and its reflected image'. $(4,6) \rightarrow'(-6,-4)$

STEP 8

Once more, we can see that the x-coordinate and y-coordinate of point have been negated to obtain the coordinates of point'. This confirms that the reflection is over the origin.

STEP 9

The rule of reflection over the origin is that the coordinates of any point (x, y) become (-x, -y) after reflection.
The reflection of the triangle CDE over the origin is the triangle C'D'E' with C'(-8,-3), D'(-12,5),'(-6,-4).
The rule of reflection is over the origin.

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QuestionFind the reflection rule for triangle $C(3,8), D(5,12), E(4,6)$ to $C'(-8,-3), D'(-12,5), E'(-6,-4)$ .

Studdy Solution

STEP 1

Assumptions1. The coordinates of the original triangle are C(3,8), D(5,12),(4,6) . The coordinates of the reflected image are C'(-8,-3), D'(-12,5),'(-6,-4)

STEP 2

We can start by comparing the coordinates of the original points and their reflected images. This will help us determine the rule of reflection.

STEP 3

Let's compare the coordinates of point C and its reflected image C'. $C(3,8) \rightarrow C'(-8,-3)$

STEP 4

We can see that the x-coordinate and y-coordinate of point C have been negated to obtain the coordinates of point C'. This suggests that the reflection might be over the origin.

STEP 5

To confirm this, let's compare the coordinates of point D and its reflected image D'. $(5,12) \rightarrow D'(-12,5)$

STEP 6

Again, we can see that the x-coordinate and y-coordinate of point D have been negated to obtain the coordinates of point D'. This further supports the idea that the reflection might be over the origin.

STEP 7

Finally, let's compare the coordinates of point and its reflected image'. $(4,6) \rightarrow'(-6,-4)$

STEP 8

Once more, we can see that the x-coordinate and y-coordinate of point have been negated to obtain the coordinates of point'. This confirms that the reflection is over the origin.

STEP 9

The rule of reflection over the origin is that the coordinates of any point (x, y) become (-x, -y) after reflection.
The reflection of the triangle CDE over the origin is the triangle C'D'E' with C'(-8,-3), D'(-12,5),'(-6,-4).
The rule of reflection is over the origin.

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QuestionFind the reflection rule for triangle C(3,8),D(5,12),E(4,6)C(3,8), D(5,12), E(4,6)C(3,8),D(5,12),E(4,6) to C′(−8,−3),D′(−12,5),E′(−6,−4)C'(-8,-3), D'(-12,5), E'(-6,-4)C′(−8,−3),D′(−12,5),E′(−6,−4).

Studdy Solution

STEP 1

Assumptions1. The coordinates of the original triangle are C(3,8), D(5,12),(4,6) . The coordinates of the reflected image are C'(-8,-3), D'(-12,5),'(-6,-4)

STEP 2

We can start by comparing the coordinates of the original points and their reflected images. This will help us determine the rule of reflection.

STEP 3

Let's compare the coordinates of point C and its reflected image C'.C(3,8)→C′(−8,−3)C(3,8) \rightarrow C'(-8,-3)C(3,8)→C′(−8,−3)

STEP 4

We can see that the x-coordinate and y-coordinate of point C have been negated to obtain the coordinates of point C'. This suggests that the reflection might be over the origin.

STEP 5

To confirm this, let's compare the coordinates of point D and its reflected image D'.(5,12)→D′(−12,5)(5,12) \rightarrow D'(-12,5)(5,12)→D′(−12,5)

STEP 6

Again, we can see that the x-coordinate and y-coordinate of point D have been negated to obtain the coordinates of point D'. This further supports the idea that the reflection might be over the origin.

STEP 7

Finally, let's compare the coordinates of point and its reflected image'.(4,6)→′(−6,−4)(4,6) \rightarrow'(-6,-4)(4,6)→′(−6,−4)

STEP 8

Once more, we can see that the x-coordinate and y-coordinate of point have been negated to obtain the coordinates of point'. This confirms that the reflection is over the origin.

STEP 9

The rule of reflection over the origin is that the coordinates of any point (x, y) become (-x, -y) after reflection.The reflection of the triangle CDE over the origin is the triangle C'D'E' with C'(-8,-3), D'(-12,5),'(-6,-4).The rule of reflection is over the origin.

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QuestionFind the reflection rule for triangle $C(3,8), D(5,12), E(4,6)$ to $C'(-8,-3), D'(-12,5), E'(-6,-4)$ .

Let's compare the coordinates of point C and its reflected image C'. $C(3,8) \rightarrow C'(-8,-3)$

To confirm this, let's compare the coordinates of point D and its reflected image D'. $(5,12) \rightarrow D'(-12,5)$

Finally, let's compare the coordinates of point and its reflected image'. $(4,6) \rightarrow'(-6,-4)$

The rule of reflection over the origin is that the coordinates of any point (x, y) become (-x, -y) after reflection.
The reflection of the triangle CDE over the origin is the triangle C'D'E' with C'(-8,-3), D'(-12,5),'(-6,-4).
The rule of reflection is over the origin.