Question

Triangle ABC has vertices A(-2,2), B(-1,-3), and C(4,0) . Find the coordinates of the vertices of A', B' and C', the image of ABC after the transformation rx-axis

Answer 1

A'(-2,-2),B'(-1,3),C'(4,0)

Step-by-step explanation:

Given triangle ABC with vertices as defined below:

`A\mleft(-2,2\mright),B\mleft(-1,-3\mright),\; C\mleft(4,0\mright)`

The transformation 'rx-axis' is a reflection over the x-axis.

When you reflect a point (x,y) over the x-axis, the transformation is given below:

`r_{x-\text{axis}}\colon(x,y)\to(x,-y)`

That is, the x coordinate remains the same but the y-coordinate changes to its opposite.

Therefore, the coordinates of the vertices of A', B' and C' will be:

`A^(\prime)\mleft(-2,-2\mright),B^(\prime)\mleft(-1,3\mright),C^(\prime)\mleft(4,0\mright)`