Given a point (-2,5determine a point that satisfies the specified symmetry.
1. Origin (2,-5)
2. y-axis (2,5)
3. x-axis (-2,-5)
4. y=x ?
Could you check if 1-3 is correct and could you help me on #4
To determine a point that satisfies the specified symmetry, you need to understand the concept of symmetry and how it applies to each case.
1. Symmetry with respect to the origin:
If a point (x, y) is symmetric with respect to the origin, then its symmetric point will have coordinates (-x, -y).
Given the point (-2, 5), if we take the opposite of both x and y coordinates, we get (2, -5). So, the point (2, -5) satisfies the symmetry with respect to the origin.
Therefore, option 1 is correct.
2. Symmetry with respect to the y-axis:
If a point (x, y) is symmetric with respect to the y-axis, then its symmetric point will have coordinates (-x, y).
Given the point (-2, 5), if we take the opposite of the x coordinate, we get (2, 5). So, the point (2, 5) satisfies the symmetry with respect to the y-axis.
Therefore, option 2 is correct.
3. Symmetry with respect to the x-axis:
If a point (x, y) is symmetric with respect to the x-axis, then its symmetric point will have coordinates (x, -y).
Given the point (-2, 5), if we take the opposite of the y coordinate, we get (-2, -5). So, the point (-2, -5) satisfies the symmetry with respect to the x-axis.
Therefore, option 3 is correct.
4. Symmetry with respect to y = x:
The line y = x represents the diagonal line that passes through the points where x = y. To find a point that satisfies this symmetry, you need to reflect the given point across this line.
Given the point (-2, 5), to find its symmetric point with respect to y = x, reverse its coordinates to get (5, -2).
Therefore, the point (5, -2) satisfies the symmetry with respect to y = x.
I hope this explanation helps!