Question

.......................1) Translation 5 units right, 1 unit down2) Reflection across y-axis3) 90 rotation counterclockwise4) Translation 5 units left and 1 unit up

Answer 1

Both shapes seem equal, this means that the transformation that occurred between both figures is a rigid transformation.

To determine the transformation from the preimage ABC to the image A'B'C' you have to compare the coordinates between two corresponding points, for example:

B(4,2) and B'(-1,3)

The transformation vas a translation, you can tell this because the image is pointing in the same direction as the preimage.

To determine the number of units it was translated you have to calculate the difference between the coordinates of the preimage and the coordinates of the image:

The horizontal movement was achieved by changing the x-coordinates of the points

$x_B-x_{B^{\prime}}=-1-4=-5$

The negative value indicates that the movement was to the left.

The vertical movement was achieved by changing the y-coordinates of the vertices of the preimage.

$y_{B^{\prime}}-y_B=3-2=1$

The positive value indicates that the movement was done upwards.

So the preimage ABC was moved 5 units to the left and 1 unit up