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What series of transformations from △ABC to △DEF shows that △ABC ≌ △DEF?


a). a reflection across the y-axis followed by a translation of 1 unit right and 2 units up


b). a clockwise rotation of 90º about the origin followed by a translation of 4 units right and 4 units up


c). a reflection across the x-axis followed by a translation of 1 unit right and 1 unit down


d). a reflection across the line y=x followed by a positive rotation of 270º about the center

What series of transformations from ABC to DEF shows that ABC DEFa a reflection across the yaxis followed by a translation of 1 unit right and 2 units upb a clo class=

Respuesta :

We start with

[tex] A = (-4,1)\quad B=(-6,5)\quad C=(-1,2)[/tex]

If we perform a reflection across the x-axis, we will change the sign of all the y coordinates:

[tex] A' = (-4,-1)\quad B'=(-6,-5)\quad C'=(-1,-2)[/tex]

If we perform a translation of 1 unit right, we will increase the x coordinates by 1:

[tex] A'' = (-3,-1)\quad B''=(-5,-5)\quad C''=(0,-2)[/tex]

If we perform a translation of 1 unit dpwn, we will decrease the y coordinates by 1, and the coordinates of the vertices will match those of the new triangle:

[tex] A''' \equiv D = (-3,-2)\quad B'''\equiv E=(-5,-6)\quad C'''\equiv F=(0,-3)[/tex]

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