Translate triangle A by vector (-3,1) to give triangle B. Then roste your triangle B 180 degrees around the origin to give triangle C. Describe fully the single transformation that maps triangle A onto triangle C

Triangle C is in the first quadrant and this transformation is done by translating triangle A by a vector (-3,1) and then rotating the triangle B by 180 degrees.

Given :

The following steps can be used to describe the transformation that maps triangle A onto triangle C:

Step 1 - Triangle A is given in the fourth quadrant.

Step 2 - Now, as per the given data translate triangle A by a vector (-3,1) which means the triangle shift in the negative x-axis by a factor of 3 and also shift downwards in the negative y-axis by a factor of 1.

The resulting triangle is in the third quadrant which is triangle B.

Step 3 - Now, rotate the triangle B by 180 degrees. So, the resulting triangle is triangle C which is in the first quadrant.

For more information, refer to the link given below:

link

The first transformation is a reflection across the x-axis, then a shift one unit down. Finally, a reflection acroos the line x = 1.5. These transformations give figure B.

To get figure C, we just need to do a 180° rotation across the origin. Or, you can see this transformation as a reflection acroos the origin, it would be the same result.