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Reflect the point (4,-7) across the x-axisreflect the point (4,-7) across the y-axis

User MUHAHA
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Hello there. In order to reflect the point across the x-axis, we have to remember some properties about reflections on the cartesian plane.

Given the cartesian plane and the point (4, -7) as follows:

You want to determine a point that has the same distance from the x-axis in the opposite quadrant to it.

In this case, the point is in the fourth quadrant and reflecting across the x-axis, you find that the point must be in the first quadrant.

Another thing that will happen is that the point will have the same x-coordinate, hence you only have to determine the y-coordinate.

Having the same x-coordinate means that the point are lined with respect to the vertical line x.

Hence the coordinate of the point is simply: (x, -y).

In our case, we get


(4,7)

This is the point we get by reflecting it across the x-axis:

Another way of finding it is by applying the rotation matrix transformation:


\begin{bmatrix}{\cos(\theta)} & \sin(\theta){} \\ {-\sin(\theta)} & {\cos(\theta)}\end{bmatrix}

Reflect the point (4,-7) across the x-axisreflect the point (4,-7) across the y-axis-example-1
Reflect the point (4,-7) across the x-axisreflect the point (4,-7) across the y-axis-example-2
User Thijs Koerselman
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7.4k points