Given: The coordinate of triangle LMN as
[tex]\begin{gathered} L(0,-3) \\ M(2,1) \\ N(7,0) \end{gathered}[/tex]
To Determine: The coordinates of the image, L'M'N' under the translation 2 units to the left and 4 units up
The translation rule for a translation of of a units to the left is
[tex](x,y)\rightarrow(x+a,y)[/tex]
The translation rule for translation of b units up is
[tex](x,y)\rightarrow(x,y+b)[/tex]
Therefore, the translation rule of a units to the left and b units up is
[tex](x,y)\rightarrow(x+a,y+b)[/tex]
Applying the rule to given translation of 2 units to the left and 4 units up would be
[tex](x,y)\rightarrow(x+2,y+4)[/tex]
Now, we apply the rule to get the coordinates of the image as shown below
[tex]\begin{gathered} L(0,-3)\rightarrow L^{\prime}(0+2,-3+4)=L^{\prime}(2,1) \\ M(2,1)\rightarrow M^{\prime}(2+2,1+4)=M^{\prime}(4,5) \\ N(7,0)\rightarrow N^{\prime}(7+2,0+4)=N^{\prime}(9,4) \end{gathered}[/tex]
Hence, the coordinate of the image is
L'(2,1)
M' (4,5)
N' (9,4)
