Respuesta :

After translation, the new triangle will be [tex]\Delta X'Y'Z'[/tex], where the coordinates of [tex]X'[/tex], [tex]Y'[/tex] and [tex]Z'[/tex] are given by: [tex]X'(2,7)[/tex], [tex]Y'(5,-2)[/tex] and [tex]Z'(4,7)[/tex].

What will be the new coordinates of a point after translation?

  • In translation, the original set of axes moves parallelly toward left/right/up/down.
  • If the coordinates of a point with respect to the original set of axes are [tex]P(x,y)[/tex], then, after translating the axes [tex]h[/tex]n units right and [tex]k[/tex] units up, the new coordinates will be [tex]P'(x+h,y+k)[/tex].

Here, we are to translate the triangle [tex]\Delta XYZ[/tex] 2 units to the right and 4 units to the up.

The new coordinates of the point [tex]X(0,3)[/tex] will be [tex]X'(0+2,3+4)[/tex] i.e., [tex]X'(2,7)[/tex].

The new coordinates of the point [tex]Y(3,-6)[/tex] will be [tex]X'(3+2,-6+4)[/tex] i.e., [tex]Y'(5,-2)[/tex].

The new coordinates of the point [tex]Z(1,3)[/tex] will be [tex]X'(1+2,3+4)[/tex] i.e., [tex]Z'(3,7)[/tex].

Therefore, after translation, the new triangle will be [tex]\Delta X'Y'Z'[/tex], where the coordinates of [tex]X'[/tex], [tex]Y'[/tex] and [tex]Z'[/tex] are given by: [tex]X'(2,7)[/tex], [tex]Y'(5,-2)[/tex] and [tex]Z'(4,7)[/tex].

To know more about translation, refer: https://brainly.com/question/12861087

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