Question

Help me solve this problem! Thank you! Only answer if you understand

Answer 1

Composite transformation:

$(D_2\circ T_{<-5,-3>})$

1. Translation 5 units to the left and 3 units down:

$(x,y)\rightarrow(x-5,y-3)$

Apply the rule above to vertices of given triangle:

$\begin{gathered} M(3,5)\rightarrow M^{\prime}(3-5,5-3) \\ M^{\prime}(-2,2) \\ \\ \\ N(-1,4)\rightarrow N^{\prime}(-1-5,4-3) \\ N^{\prime}(-6,1) \\ \\ \\ O(1,8)\rightarrow O^{\prime}(1-5,8-3) \\ O^{\prime}(-4,5) \end{gathered}$

2. Dilation with factor 2:

$(x,y)\rightarrow(2x,2y)$

Apply the rule above to vertices M'N'O':

$\begin{gathered} M^{\prime}(-2,2)\rightarrow M^{\prime}^{\prime}(2*-2,2*2) \\ M^{\prime}^{\prime}(-4,4) \\ \\ N^{\prime}(-6,1)\rightarrow N^{\prime}^{\prime}(2*-6,2*1) \\ N^{\prime}^{\prime}(-12,2) \\ \\ O^{\prime}(-4,5)\rightarrow O^{\prime}^{\prime}(2*-4,2*5) \\ O^{\prime}^{\prime}(-8,10) \end{gathered}$

Then, the vertices of image after the composite transformation are:

M''(-4,4)

N''(-12,2)

O''(-8,10)

Graph: