Given the triangle ABC at points A = ( 1, - 4 ) B = ( 4, - 5 ) C = ( 6, - 3 ), and if the triangle is first reflected over the y axis, and then over the x axis, find the new point A''.

Respuesta :

Given: The coordinates of triangle ABC as

[tex]\begin{gathered} A=(1,-4) \\ B=(4,-5) \\ C=(6,-3) \end{gathered}[/tex]

To Determine: The coordinates of triangle ABC after first reflect over the y-axis and then over the x-axis

Solution

The reflection over the y-axis rule is given as

[tex](x,y)\rightarrow(-x,y)[/tex]

Let us apply the rule to the given triangle ABC

[tex]\begin{gathered} A(1,-4)\rightarrow A^{\prime}(-1,-4) \\ B(4,-5)\rightarrow B^{\prime}(-4,-5) \\ C(6,-3)\rightarrow(-6,-3) \end{gathered}[/tex]

The reflection rule over the x-axis is given as

[tex](x,y)\rightarrow(x,-y)[/tex]

Let us apply the rule to the given

[tex]\begin{gathered} A^{\prime}(-1,-4)\rightarrow A^{\prime}^{\prime}(-1,4) \\ B^{\prime}(-4,-5)\rightarrow B^{\prime}^{\prime}(-4,5) \\ C^{\prime}(-6,-3)\rightarrow C^{\prime}^{\prime}(-6,3) \end{gathered}[/tex]

Hence, the new point of A'' = (-1, 4)