A four sided figure WXYZ is shown on the coordinate plane. The figure is then reflected across the y-axis. Which point of the figure above will end up in quadrant 1?
To reflect a point across the $y$-axis, we negate the $x$-coordinate while keeping the $y$-coordinate the same. Therefore, point $W$ will end up in quadrant $\boxed{1}$.
To find out which point of the figure WXYZ will end up in quadrant 1 after reflecting it across the y-axis, we need to consider the coordinates of the points.
Quadrant 1 is the top right-hand side of the coordinate plane, where both the x-coordinate and y-coordinate are positive.
Since the figure is reflected across the y-axis, the x-coordinate of each point will be negated (multiplied by -1), while the y-coordinate remains the same.
Let's consider each point:
- Point W: (xW, yW)
- Point X: (xX, yX)
- Point Y: (xY, yY)
- Point Z: (xZ, yZ)
After reflecting across the y-axis, the x-coordinate of each point will change. The new coordinates will be:
- Point W': (-xW, yW)
- Point X': (-xX, yX)
- Point Y': (-xY, yY)
- Point Z': (-xZ, yZ)
To determine which point will end up in quadrant 1, we need to check if the new x-coordinate is positive.
If -xW > 0, then W' will be in quadrant 1.
If -xX > 0, then X' will be in quadrant 1.
If -xY > 0, then Y' will be in quadrant 1.
If -xZ > 0, then Z' will be in quadrant 1.
So, we need to find the x-coordinate of each point and determine if it is positive or negative to identify which point will end up in quadrant 1.