Maintaining Mathematical Proficiency
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Plot points and observe the changes.
It is a reflection about the origin.
Let's check each quadrant one by one.
In Quadrant I, both x and y are positive numbers. Let's choose (2,2) as our point. Then we multiply both coordinates by a negative number, let's use -1. This reverses the point's signs so we get (-2,-2). Let's plot these points.
In Quadrant II, x is negative and y is positive. Let's choose (-1,1) as our point. Then we multiply both coordinates by a negative number, let's use -1. This reverses the point's signs so we get (1,-1). Let's plot these points.
In Quadrant III, both x and y are negative numbers. Let's choose (-3,-3) as our point. Then we multiply both coordinates by a negative number, let's use -1. This reverses the point's signs so we get (3,3). Let's plot these points.
In Quadrant IV, x is positive and y is negative. Let's choose (4,-4) as our point. Then we multiply both coordinates by a negative number, let's use -1. This gives the point (-4,4). Let's plot these points.
In each case, multiplying the point by a negative number carries the point diagonally across the origin to the new point. This is called a reflection about the origin.