Write the coordinates of point R' after the following reflection: reflection across the x-axis. (2024)

FAQs

How to find the coordinates after a reflection over the x-axis? ›

In other words, the rule for a reflection over the x -axis is: ( x , y ) becomes ( x , - y ) with a reflection over the x-axis. We can see that a coordinate on the reflected image has become negative, but this time it's the x value instead of the y value. The rule in this case is ( x , y ) becomes ( - x , y ) .

When you reflect a point across the x-axis, the x-coordinate remains the same, but the y-coordinate is taken to be the additive inverse. The reflection of point (x, y) across the x-axis is (x, -y).

To reflect an equation over the x-axis, simply multiply the output variable by negative one: y = f ( x ) → y = − f ( x ) .

Summary: The coordinates of the point (-1, 6) after a reflection across the x-axis are (-1, -6).

If you reflect over the line y = -x, the x-coordinate and y-coordinate change places and are negated (the signs are changed). the line y = x is the point (y, x). the line y = -x is the point (-y, -x).

To reflect over the x-axis, change the sign on the y coordinates of selected given points. Reflections over the y-axis require the x coordinated to be negated. Reflections over the origin require that both the x and y coordinates be negated, and to reflect over the line y=x, swap x and y.

When a point is reflected along the y axis, the X coordinate becomes the opposite number and the y coordinate stays the same. Likewise, when a point is reflected along the X axis, the X coordinate stays the same and the y coordinate becomes the opposite. The x coordinate is opposite.

Expert-Verified Answer

The coordinates of the image of vertex R after a reflection across the y-axis is (3, 4).

Find the intersection point of the given line and the perpendicular bisector. This point is the center of reflection. Use the center of reflection to calculate the distance between the given point and the center. Reflect the point across the center using the distance and direction.

The reflection of the point (x, y) across the x-axis is the point (x, -y). Reflection over the y axis: When you reflect a point across the y-axis, the y-coordinate remains the same, but the x-coordinate is transformed into its opposite (its sign is changed).

What is the reflection across the x-axis of F x )= x2? ›

To reflect a graph, f(x) over the x-axis, you take -f(x). So if f(x)=x^2, then -f(x) is -x^2.

When a point is reflected across the line y = x, the x-coordinates and y-coordinates change their place. Similarly, when a point is reflected across the line y = -x, the x-coordinates and y-coordinates change their place and are negated. Therefore, The reflection of the point (x, y) across the line y = x is (y, x).

A reflection over the line y = -x follows the rule (x, y) → (-y, -x). This means reverse the order of the coordinates and reverse the signs. (-2, 6) would become (-6, 2).

Summary: The coordinates of the image of vertex F after a reflection across the line y = -x is (3, -1).

Expert-Verified Answer

The coordinates of the image of point J after a reflection across the x-axis include the following: J' (8, -7).

Expert-Verified Answer

The coordinates of A' after reflection across the line x = 3 is (3,2).

Expert-Verified Answer

A reflection across the line x = 1 involves changing the x-coordinate of each point but keeping the y-coordinate the same. The new coordinate for each vertex after the reflection will be (2*1 - x, y). This is like 'flipping' the figure over the line x = 1.