Given a point (-2,5), determine a point that satisfies the specified symmetry.
1.)Origin
2.)y-axis
3.)x-axis
4.)y=x
To find a point that satisfies a specified symmetry, you need to understand how that symmetry is defined. Let's look at each option and determine the point that satisfies the specified symmetry.
1.) Origin:
To find a point that satisfies symmetry with the origin, you need to reflect the given point (-2, 5) across the origin (0, 0). To do this, you can reverse the signs of the x and y coordinates.
So, the point that satisfies symmetry with the origin is: (2, -5).
2.) Y-axis:
To find a point that satisfies symmetry with the y-axis, you need to reflect the given point (-2, 5) across the y-axis. To do this, you simply reverse the sign of the x-coordinate while keeping the y-coordinate the same.
So, the point that satisfies symmetry with the y-axis is: (2, 5).
3.) X-axis:
To find a point that satisfies symmetry with the x-axis, you need to reflect the given point (-2, 5) across the x-axis. To do this, you reverse the sign of the y-coordinate while keeping the x-coordinate the same.
So, the point that satisfies symmetry with the x-axis is: (-2, -5).
4.) y = x:
To find a point that satisfies symmetry with the line y = x, you need to find the line perpendicular to y = x that passes through the given point (-2, 5). To do this, you swap the x and y coordinates.
So, the point that satisfies symmetry with the line y = x is: (5, -2).
I hope this explanation helps you understand how to determine points that satisfy specific symmetries.