Question

triangle ABV has coordinates at A(2,10), B(3,-4) and C(-3,1). write the new coordinates after the triangle is reflected over the x-axis. write the new coordinates after the triangle is reflected over the y-axis.

Answer 1

When a figure is reflected over one of the axis there is only a change on the sign of one of the coordinates.

When the reflection is done over the x-axis the transformation follows the rule

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

When the reflection is done over the y-axis the transformation follows the rule

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

According to this if we reflect triangle ABC over the x axis then

$\begin{gathered} A(2,10)\rightarrow A^{\prime}(2,-10) \\ B(3,-4)\rightarrow B^{\prime}(3,4) \\ C(-3,1)\rightarrow C^{\prime}(-3,-1) \end{gathered}$

If we reflect the triangle over the y axis

$\begin{gathered} A(2,10)\rightarrow A^{\prime}(-2,10) \\ B(3,-4)\rightarrow B^{\prime}(-3,-4) \\ C(-3,1)\rightarrow C^{\prime}(3,1) \end{gathered}$