Question

The endpoints of segment CD are C(1, 2) and D(5, 4). Graph the image of segment CD after the composition of transformations. C(1, 2) and D(5, 4) Translation: (x, y) = (x - 4, y) Reflection: over the x-axis

Answer 1

Transformations

We are given the endpoints of segment CD C(1,2) D(5,4)

It's required to apply two transformations of the segment CD, as follows.

First, we apply (x,y) => (x-4,y)

For point C(1,2) =>C'(1-4,2)=>C'(-3,2)

For point D(5,4)=>D'(5-4,4)=>D'(1,4)

Now we apply a reflection over the x-axis.

A reflection over the x-axis maps point (x,y) to (x,-y).

For point C'(-3,2)=>C''(-3,-2)

For point D'(1,4)=>D''(1,-4)

The segment C''D'' will be represented in the graph below