How to Reflect a Shape In the Line y = -x Using Cartesian Coordinates (Mathematics Lesson)
How to Reflect a Shape in the Line y = -x Using Cartesian CoordinatesTo reflect a shape in the line y = -x using Cartesian coordinates, if a point on the shape has coordinates (x,y), the reflected point has coordinates (-y,-x).
Method of How to Reflect a Point in Line y = -x Using Cartesian CoordinatesFor each vertex (corner) of the shape:
Step 1: Find the Cartesian coordinate of the vertex.
Step 2: Find the Cartesian coordinate of the reflected vertex by swapping the x-coordinate and the y-coordinate around and changing the sign of both coordinates.
A Real Example of How to Reflect a Shape in the Line y = -x Using Cartesian CoordinatesQuestion: Reflect the shape below in the line y = -x.
Step 1: Find the Cartesian coordinates of each vertex.
|Vertex of Object||Coordinate|
Step 2: Find the Cartesian coordinate of the reflected vertex by swapping the x coordinate and the y coordinate around and changing the sign of both coordinates.
|Vertex of Object||Coordinate||Vertex of Image||Coordinate|
With all the vertices reflected, we can draw in the reflected shape:
This is the shape reflected in the line y = -x.
NoteFINDING THE CARTESIAN COORDINATES OF A POINT
- The coordinate on the left is the x-coordinate.
It describes how far along the x-axis, or how far across, the point is.
- The co-ordinate on the right is the y-coordinate.
It describes how far up the y-axis, or how far up, the point is.
WHAT IS THE LINE y = -x
y = -x is a linear equation.
y = -x represents a diagonal line that goes through the origin. It goes from top left to bottom right.
It goes halfway between the x-axis and the y-axis. y = -x is at 45° to both axes.
WHAT IS A REFLECTION?
A reflection transforms a shape so that it becomes a mirror image of itself.
The orginal shape is called the object, the reflected shape is called the image.
A reflection is a type of transformation.