Given:
Triangle XYZ has translated 9 units to the right and 5 units down.
The objective is,
a) To find the coordinates of translated triangle ∆X'Y'Z'.
b) To find the general rule for translation mapping.
Explanation:
a)
Since 9 unit is translated to the right, add 9 to all the three coordinates of the triangle. And 5 units moved down, subtract 5 from all the three coordinates of the triangle.
The coordinates of ∆X'Y'Z' are,
[tex]\begin{gathered} X(-7,4)\rightarrow X(-7+9,4-5)\rightarrow X^{\prime}(2,-1) \\ Y(-3,2)\rightarrow Y(-3+9,2-5)\rightarrow Y^{\prime}(6,-3) \\ Z(-8,1)\rightarrow Z(-8+9,1-5)\rightarrow Z^{\prime}(1,-4) \end{gathered}[/tex]
Hence, the final coordinates of ∆X'Y'Z' are X'(2,-1), Y'(6,-3), and Z'(1,-4).
b)
The general rule that describes the translation will be the addition of 9 for all x values as it is translated into 9 units to the right.
Similarly, the subtraction of 5 units for all y values as it is translated 5 units down.
Hence, the correct option is (x,y) → (x+9, y-5).
