Question

write the coordinates of the vertices after a reflection over the line y = -x.
e(( ), )
f(( ), )
g(( ), )

Explanation:

Step1: Find original coordinates

First, identify the original coordinates of \( E \), \( F \), and \( G \) from the graph.

• \( E \) is at \( (1, 0) \) (since it's 1 unit right on the x - axis and 0 on the y - axis).
• \( F \) is at \( (9, 0) \) (9 units right on the x - axis and 0 on the y - axis).
• \( G \) is at \( (0, 10) \) (0 on the x - axis and 10 units up on the y - axis).

Step2: Apply reflection over \( y=-x \)

The rule for reflecting a point \( (x,y) \) over the line \( y = -x \) is \( (x,y)\to(-y,-x) \).

• For point \( E(1,0) \):

Using the rule \( (x,y)\to(-y,-x) \), substitute \( x = 1 \) and \( y = 0 \). We get \( E'(-0,-1)=(0, - 1) \).

• For point \( F(9,0) \):

Substitute \( x = 9 \) and \( y = 0 \) into the rule \( (x,y)\to(-y,-x) \). We get \( F'(-0,-9)=(0, - 9) \).

• For point \( G(0,10) \):

Substitute \( x = 0 \) and \( y = 10 \) into the rule \( (x,y)\to(-y,-x) \). We get \( G'(-10,-0)=(-10,0) \).

Answer:

\( E'(0, - 1) \), \( F'(0, - 9) \), \( G'(-10,0) \)