Given the point (-5,-2)
symmetric to this point with respect to the x-axis
When a point reflects in x axis then
(x,y) -> (x, -y)
So symmetric with respect to the x-axis (-5,-2) -> (-5, 2)
symmetric to this point with respect to the y-axis
When a point reflects in y axis then
(x,y) -> (-x, y)
So symmetric with respect to the y-axis(-5,-2) -> (5, -2)
symmetric to this point with respect to the origin
When a point reflects in origin then
(x,y) -> (-x, -y)
So symmetric with respect to the origin (-5,-2) -> (5, 2)
You can use the fact that the points are called symmetric if they're like reflected over a line as if there is a mirror placed and the symmetric point is like the reflection image of the original point.
The symmetric points for (-5.-2) for given cases are
Let the point be (x,y)
Case 1: Symmetry with respect to x-axis
The point becomes (x, -y) as the point flips itself up or down which changes its y coordinate to negative of whatever it was previously. And no motion is done horizontally so no change in x coordinate.
Case 2: Symmetry with respect to y-axis
The point becomes (-x, y) as the point flips itself left or right which changes its x coordinate to negative of whatever it was previously. And no motion is done vertically so no change in y coordinate.
Case 3: Symmetry with respect to origin
Origin is point at (0,0)
Symmetry with this is a bit ill defined. We use a slant line as if its a diagonal of a square. The point is reflected to its diagonally opposite quadrant to whatever coordinate it belongs to.
Since diagonally opposite reflection causes both x and y axis to become negative of what it was before, thus,
The point becomes (-x,-y)
Using the above conclusions, we have:
The symmetric points for (-5.-2) for given cases are
Learn more about reflection over an axis here:
brainly.com/question/2235973
