Reflection

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Reflection is a transformation where an object's image is obtained on the other side of a mirror line (axis of reflection). The distance of the image from the mirror line equals the distance of the ob…

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An invariant point is a point that remains unchanged after reflection. A point is invariant with respect to a given line if and only if it lies on that line. For example, any point on the x-axis is in…

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The reflection of point P(x,y) in the x-axis is P'(x,-y). This is written as Mx(x,y) = (x,-y). The x-coordinate remains the same, but the y-coordinate changes sign.

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The reflection of point P(x,y) in the y-axis is P'(-x,y). This is written as My(x,y) = (-x,y). The y-coordinate remains the same, but the x-coordinate changes sign.

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Using the formula Mx(x,y) = (x,-y), the reflection of (3,-5) in the x-axis is (3,-(-5)) = (3,5). The x-coordinate stays 3, and the y-coordinate changes from -5 to +5.

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Using the formula My(x,y) = (-x,y), the reflection of (-2,4) in the y-axis is (-(-2),4) = (2,4). The x-coordinate changes from -2 to +2, and the y-coordinate stays 4.

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The reflection of point P(x,y) in the origin is P'(-x,-y). This is written as M0(x,y) = (-x,-y). Both coordinates change signs.

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Using the formula M0(x,y) = (-x,-y), the reflection of (4,-3) in the origin is (-4,-(-3)) = (-4,3). Both coordinates change signs: 4 becomes -4, and -3 becomes 3.