Describe the following reflections or translation in words
1.(x,y)--->(x,-y)
2.(x,y)-->(-y,-x)
3.(x,y)-->(x 4,y-4)
1. reflect through the x-axis
2. reflect through (0,0)
3. a translation, but you are missing a sign.
1. The first transformation reflects a point (x, y) across the x-axis. This means that the x-coordinate remains the same, but the y-coordinate changes sign. So, the new point becomes (x, -y).
2. The second transformation reflects a point (x, y) across the origin (0, 0) and then rotates it 90 degrees counterclockwise. This transformation swaps the x-coordinate with the negative y-coordinate and negates both coordinates. So, the new point becomes (-y, -x).
3. The third transformation translates a point (x, y) to the right by 4 units and down by 4 units. So, the x-coordinate is increased by 4 and the y-coordinate is decreased by 4. The new point becomes (x + 4, y - 4).
1. The first transformation is a reflection across the x-axis. This means that for any point (x,y), the new point will have the same x-coordinate but a new y-coordinate that is the opposite of the original y-coordinate. For example, if we have the point (3,2), its reflection across the x-axis would be (3,-2).
2. The second transformation is a reflection across the line y = -x. This means that for any point (x,y), the new point will have the same distance from the line y = -x, but on the opposite side. The coordinates of the new point will be (-y,-x). For example, if we have the point (4,2), its reflection across the line y = -x would be (-2,-4).
3. The third transformation is a translation, which means shifting the point horizontally and/or vertically. In this case, we are shifting the point (x,y) to the new point (x+4, y-4). The x-coordinate of the new point is obtained by adding 4 to the original x-coordinate, while the y-coordinate is obtained by subtracting 4 from the original y-coordinate. For example, if we have the point (2,5), its translation (shift) by (4,-4) would be (2+4, 5-4), resulting in the point (6,1).