Question

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''.

Answer 1

Given: The coordinates of triangle ABC as

`\begin{gathered} A=(1,-4) \\ B=(4,-5) \\ C=(6,-3) \end{gathered}`

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

`(x,y)\rightarrow(-x,y)`

Let us apply the rule to the given triangle ABC

`\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}`

The reflection rule over the x-axis is given as

`(x,y)\rightarrow(x,-y)`

Let us apply the rule to the given

`\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}`

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