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Points M (3,4) and T(-2, 3) form MT. The translation (x, y) -> (x + h,y + k) is applied to MT', such that M' (7, 1) and I' (2, 0).
Complete the algebraic description of the translation.
(x,y) -> (x+ h,y + k)

h=
k=



Answer :

semsee45

Answer:

(x, y) → (x + 4, y - 3)

h = 4

k = -3

Step-by-step explanation:

Given points:

  • M = (3, 4)
  • M' = (7, 1)
  • T = (-2, 3)
  • T' = (2, 0)

Given translation:

(x, y) → (x+h, y+k)

To find the value of h, subtract the x-values of points M and T from the x-values of points M' and T':

[tex]\begin{aligned}\implies h&=x_{M'}-x_M\\&=7-3\\&=4\end{aligned}[/tex]

[tex]\begin{aligned}\implies h&=x_{T'}-x_T\\&=2-(-2)\\&=4\end{aligned}[/tex]

To find the value of k, subtract the y-values of points M and T from the y-values of points M' and T':

[tex]\begin{aligned}\implies k&=y_{M'}-y_M\\&=1-4\\&=-3\end{aligned}[/tex]

[tex]\begin{aligned}\implies k&=y_{T'}-y_Y\\&=0-3\\&=-3\end{aligned}[/tex]

Therefore the algebraic description of the translation is:

(x, y) → (x + 4, y - 3)

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