Question

4. I The coordinates of ΔLMN are L(0,-3), M(2,1) and N(7,0). Right the coordinates of L’,M’, and N’ when ΔLMN is under a translation 2 units to the left and 4 units up

Answer 1

Given: The coordinate of triangle LMN as

`\begin{gathered} L(0,-3) \\ M(2,1) \\ N(7,0) \end{gathered}`

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

`(x,y)\rightarrow(x+a,y)`

The translation rule for translation of b units up is

`(x,y)\rightarrow(x,y+b)`

Therefore, the translation rule of a units to the left and b units up is

`(x,y)\rightarrow(x+a,y+b)`

Applying the rule to given translation of 2 units to the left and 4 units up would be

`(x,y)\rightarrow(x+2,y+4)`

Now, we apply the rule to get the coordinates of the image as shown below

`\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}`

Hence, the coordinate of the image is

L'(2,1)

M' (4,5)

N' (9,4)