Answered

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Find the image C (-1,3) under the transformations T (-2,3) ° r x-axis

Sagot :

First, we have that the equation to calculate the reflection over the x-axis is:

[tex]r_x(x,y)=(x,-y)[/tex]

And the forumal for the reflection of point 'a' across the point 'p' is:

[tex]T_p(a)=(2p_1-a_1,2p_2-a_2)[/tex]

then, for the point C(-1,3), we have the following:

[tex]\begin{gathered} (T_{(-2,3)}\circ r_x)(C)=(T_{(-2,3)}\circ r_x)(-1,3)_{}_{} \\ =T_{(-2,3)}(r_x(-1,3))=T_{(-2,3)}(-1,-3)=(2(-2)-(-1),2(3)-(-3)) \\ =(-4+1,6+3)=(-3,9) \end{gathered}[/tex]

therefore, the image of C(-1,3) under the transformations is (-3,9)

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