The vertices of delta ABC are A1 1 B0 3 and C3 4 Graph the i

The vertices of delta ABC are A(-1, 1), B(0, 3), and C(3, 4). Graph the image of delta ABC after a composition of the following transformations in the order they are listed. Translation: (x. y) rightarrow (x - 3. y - 3) Reflection: in the line y = x Yes No Is the composition a glide reflection? yes No Is the image the same if the order of the transformations is switched? (reflection, then glide) The vertices of delta ABC are A(-1.1), B(0.3). and C(3, 4). Graph the image of delta ABC after a composition of the following transformations in the order they are listed. Rotation: 90 degree counterclockwise about the origin Reflection: in the y-axis Yes No If the transformations were performed reverse order (reflection, then rotation), would the final image be the same? yes No Would the reflection of delta ABC in the line y = x have produced the same final image?

Solution

new coordinates upon rotation are X= xcosA - ysinA; Y = xsinA + ycosA

here A= 90

So, X=-y and Y = x;

coordinates of point (-y,x) after reflection about y axis is (y,x)--------------(1)

final coordinates after reflection are A(1,-1);B(3,0);C(4,3)

if the process were taken in reverse manner ,(x,y)--->(-x,y)--->(-y,-x) -----------(2)

final coordinates after rotation are A(-1,1);B(-3,0);C(-4,-3)

reflection of point (x,y) on the line x=y is (y,x) -------(3)

From (1) , (2) and (3)

if transformations were performed in reverse order final image is not same and

final image would be same as reflection in line x=y.