Question

A triangle is shown.Drag graphs to the table to show the image of the triangle after it is reflected over the x-axis, the y-axis, or the line =y=x.

Answer 1

Explanation:

The first thing is to establish the points of which the triangle forms.

Now we apply the rule of reflection in each case.

1. x -axis

`P(x,y)\rightarrow P^(\prime)(x,-y)`

In this case:

`\begin{gathered} A(1,-3)\rightarrow A^(\prime)(1,3) \\ B(3,-2)\rightarrow B^(\prime)(3,2) \\ C(4,-5)\rightarrow C^(\prime)(4,5) \end{gathered}`

Therefore, the x-axis image is:

2. y-axis

`P(x,y)\rightarrow P^(\prime)(-x,y)`

In this case:

`\begin{gathered} A(1,-3)\rightarrow A^(\prime)(-1,-3) \\ B(3,-2)\rightarrow B^(\prime)(-3,-2) \\ C(4,-5)\rightarrow C^(\prime)(-4,-5) \end{gathered}`

3. y = x

`P(x,y)=P^(\prime)(y,x)`

In this case:

`\begin{gathered} A(1,-3)\rightarrow A^(\prime)(-3,1) \\ B(3,-2)\rightarrow B^(\prime)(-2,3) \\ C(4,-5)\rightarrow C^(\prime)(-5,4) \end{gathered}`