Question

transform △abc by the following transformations:

• reflect across the line y = -x
• translate 1 unit to the right and 2 units down.

identify the final coordinates of each vertex after both transformations.

Explanation:

Step1: Find reflection rule for \(y = -x\)

The rule for reflecting a point \((x,y)\) across the line \(y=-x\) is \((x,y)\to(-y,-x)\).

Step2: Apply reflection

Let's assume the vertices of the original triangle have coordinates. After reflection across \(y = -x\), we get new - coordinates.

Step3: Apply translation rule

The translation rule of moving 1 unit to the right and 2 units down is \((x,y)\to(x + 1,y-2)\).

Step4: Calculate final coordinates

Apply the translation to the reflected - coordinates to get the final coordinates of each vertex.

(Note: Since the original coordinates of the vertices of the triangle are not given in the text, we can't provide specific numerical answers. But the general steps for solving this type of transformation problem are as above.)

Answer:

Step1: Find reflection rule for \(y = -x\)

The rule for reflecting a point \((x,y)\) across the line \(y=-x\) is \((x,y)\to(-y,-x)\).

Step2: Apply reflection

Let's assume the vertices of the original triangle have coordinates. After reflection across \(y = -x\), we get new - coordinates.

Step3: Apply translation rule

The translation rule of moving 1 unit to the right and 2 units down is \((x,y)\to(x + 1,y-2)\).

Step4: Calculate final coordinates

Apply the translation to the reflected - coordinates to get the final coordinates of each vertex.

(Note: Since the original coordinates of the vertices of the triangle are not given in the text, we can't provide specific numerical answers. But the general steps for solving this type of transformation problem are as above.)