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

ANSWER:

STEP-BY-STEP 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:

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