please explain how to do this

Question

Given A(5, –2), what are the coordinates of (T⟨−3, 4⟩∘ Rx-axis)(A)?

Answer 1

First step will be to plot the point (5,-2).

Now, the first transformation that the point will undergo is to be translated (-3, 4).

Look at (-3, 4) as if it is an ordered pair of a point. If it were an ordered pair, the x-value would be -3 and the y-value would be 4. However, it isn't an ordered pair to tell us the location of a point. This pair of #s is telling how far to move horizontally and vertically as well as in which direction.

The -3 tells us that from our original point (5, -2), we will move horizontally (left or right) 3 spaces. But which direction? Left or right? The number is NEGATIVE 3, so we move 3 spaces to the left.

Look at the x-axis. It is horizontal (left or right) and the negative value are on the left and positives on the right. So, -3 in the "x-value" spot of the ordered pair (-3, 4) tells us to move from our point on the graph to a location that is 3 spaces to the left.

Now, the positive 4 in the "y-value" spot tells us to move vertically (up or down) 4 spaces. But do we go up or down? Look at the y-axis. It is a vertical line with negatives on the bottom and positives on the top, so since our # is positive 4, we move 4 spaces up.

Starting at (5, -2), move 3 spaces left and you land on the location of (2, -2). Then move 4 spaces up and our translated point, A', is located at (2, 2).

The second transformation is to reflect the point over the x-axis. So, we are now at (2, 2). If we reflect over the x-axis, then our x-value stays the same (2), but the y-value changes, our new point should be the same distance away from the x-axis as point (2, 2) but be below the axis instead of above it. So, the newest point, A", will be located at (2, -2). That's it!