Question

a point is reflected across the y-axis.then the reflected point is reflected across the x-axis.how will the coordinates of the final point be related to the coordinates of the original point?

Answer 1

After a point with coordinates (x, y) is reflected across the y-axis and then the x-axis, the final point's coordinates will be (-x, -y), which is the inverse of the original point's coordinates.

Step-by-step explanation:

The coordinates of the final point after a point is reflected across the y-axis and then the x-axis will be inversely related to the coordinates of the original point. To illustrate, if we start with an original point (P) at coordinates (x, y), the reflection across the y-axis will change the sign of the x coordinate, resulting in point (P') with coordinates (-x, y). Subsequently, reflecting point P' across the x-axis will change the sign of the y coordinate, thus the final point (Q') will have coordinates (-x, -y).

This transformation can be visualized using a convenient coordinate system with a horizontal x-axis and a vertical y-axis. When a point is reflected across one of these axes, its respective coordinate is negated. For instance:

• Reflection across the y-axis: (x, y) becomes (-x, y)
• Reflection across the x-axis: (x, y) becomes (x, -y)

Therefore, after both reflections, the point undergoes a coordinate transformation from (x, y) to (-x, -y).

Answer 2

so when the point is reflected across the y axis, that means that the y coordinate stays the same, but the x coordinate is multiplied by -1

so when the point is reflected across the x axis, that means that the x coordinate stays the same, but the y coordinate is multiplied by -1



therefor if the original poitn was (x,y)
reflected across the y axis
(-x,y)

reflected across teh x axis
(-x,-y)


the point will be negative, or the point will be in the opposite quadrant of the original point