Question

Use complete sentences to describe the transformation that maps ABCD onto its image.

Answer 1

General Idea:

When a point or figure on a coordinate plane is moved by sliding it to the right or left or up or down, the movement is called a translation.

Say a point P(x, y) moves up or down ' k ' units, then we can represent that transformation by adding or subtracting respectively 'k' unit to the y-coordinate of the point P.

In the same way if P(x, y) moves right or left ' h ' units, then we can represent that transformation by adding or subtracting respectively 'h' units to the x-coordinate.

P(x, y) becomes $P'(x\pm h, y\pm k)$. We need to use ' + ' sign for 'up' or 'right' translation and use ' - ' sign for ' down' or 'left' translation.

Applying the concept:

The point A of Pre-image is (0, 0). And the point A' of image after translation is (5, 2). We can notice that all the points from the pre-image moves 'UP' 2 units and 'RIGHT' 5 units.

Conclusion:

The transformation that maps ABCD onto its image is translation given by (x + 5, y + 2),

In other words, we can say ABCD is translated 5 units RIGHT and 2 units UP to get to A'B'C'D'.