Question

5. AFGH with F(-6,8), G(-3,-1), and HCO, 4); reflect across the x-axis, then reflect across the line y = -x 12 a. What are the two arrow rules to show this composition? 76 b. What are the vertices of the image after the composition?

Answer 1

We are asked to reflect the vertices of a triangle first across the x-axis and then across the line y = -x. The rule for a reflection across the x-axis is the following:

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

Or

`R_x(x,y)=(x,-y)`

The rule for the reflection across the line y = -x:

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

Therefore, applying both transformations we get:

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

Applying the rule to each point.

For point F(-6,8) we get:

`(-6,8)\rightarrow(-6,-8)\rightarrow(8,6)`

For point G(-3,-1):

`(-3,-1)\rightarrow(-3,1)\rightarrow(-1,3)`

For point H(0,4) we get:

`(0,4)\rightarrow(0,-4)\rightarrow(4,0)`