Method

Reflecting a Point Across an Axis on the Coordinate Plane

Reflecting a point means making a mirror image of that point by flipping it across a certain line or axis. The following rules show how to find reflected points across a specific axis.

Point	Axis of Reflection	Procedure	Reflected Point
(x_1,y_1)	x	Change the y-coordinate to its opposite.	(x_1,- y_1)
(x_1,y_1)	y	Change the x-coordinate to its opposite.	(- x_1,y_1)
(x_1,y_1)	x and y	Change the x- and y-coordinates to their opposites.	(- x_1,- y_1)

Next, the process for reflecting points across the x-axis, the y-axis, or both, on a coordinate plane will be shown. Consider the points A, B, and C.

Point	Axis of Reflection	Reflected Point
A = (5,8)	x	?
B = (10,-5)	y	?
C = (-4,-7)	x and y	?

There are two steps to follow to reflect a point.

Find the Reflected Point

Keep the same x-coordinate of a point and change the y-coordinate to its opposite to reflect it across the x-axis. With this information, point A can be reflected across the x-axis by changing its y-coordinate 8 to its opposite, -8. A=(5, 8) ⇒ A’=(5, -8) In contrast, change the x-coordinate of a point to its opposite and keep its y-coordinate to reflect it across the y-axis. Point B can be reflected across the y-axis by changing the x-coordinate 10 to its opposite, -10 B=( 10,-5) ⇒ B’=( -10,-5) Finally, change the x-coordinate and the y-coordinate of a point to their opposites to reflect it across both the x-axis and y-axis. Therefore, reflect point C across both axes by changing its x-coordinate from -4 to 4 and its y-coordinate from -15 to 15. C=( -4, -7) ⇒ C’=( 4, 7)

Plot the Point and Its Reflection on the Coordinate Plane

Once each initial point and its reflection across a given axis are found, plot both points on the coordinate plane.

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