The point P(-1,0,1) is reflected in plane y-z=0 and has P' as its image. Determine the coordinated of point P'
To determine the coordinates of point P' after reflecting point P(-1,0,1) in the plane y-z=0, we can follow these steps:
Step 1: Understand the Reflection
The plane y-z=0 represents all the points where the y-coordinate is equal to the z-coordinate. In other words, the plane is perpendicular to the x-axis.
Step 2: Find the Mirror Point
To find the mirror point, we need to reflect point P(-1,0,1) across the plane y-z=0. Since the plane is perpendicular to the x-axis, the x-coordinate of the mirror point will remain the same.
Step 3: Apply the Reflection
To reflect the point P(-1,0,1) in the plane y-z=0, we need to invert the sign of the y-coordinate and the z-coordinate while keeping the x-coordinate the same.
Step 4: Calculate the Coordinates of P'
Let's calculate the coordinates of P' in each step:
Step 1: Understand the Reflection
The plane y-z=0 represents all the points where the y-coordinate is equal to the z-coordinate.
Step 2: Find the Mirror Point
Since the plane is perpendicular to the x-axis, the x-coordinate of the mirror point will remain the same. Therefore, the x-coordinate of P' will be -1.
Step 3: Apply the Reflection
We invert the sign of the y-coordinate and the z-coordinate of P(-1,0,1) to obtain P'(x', y', z').
Here, y' = -0 = 0 and z' = -1.
Step 4: Calculate the Coordinates of P'
Putting it all together, we have the coordinates of P' as (-1, 0, -1).
Therefore, the coordinates of point P' after reflection in the plane y-z=0 are (-1, 0, -1).