Question

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

Explanation:

Step1: Find original coordinates

First, identify the original coordinates of points D, E, F, G from the graph.

• Point D: Looking at the graph, D is at (8, -10) (since it's 8 units right on x - axis and 10 units down on y - axis)
• Point E: E is at (10, -10) (10 units right on x - axis and 10 units down on y - axis)
• Point F: F is at (10, 0) (10 units right on x - axis and 0 on y - axis)
• Point G: G is at (8, 0) (8 units right on x - axis and 0 on y - axis)

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

The rule for reflecting a point \((x,y)\) over the line \(y=x\) is to swap the x - coordinate and the y - coordinate. So, if we have a point \((x,y)\), after reflection over \(y = x\), the new point \((x',y')\) is given by \((y,x)\).

• For point D\((8, - 10)\):

After reflection over \(y=x\), we swap x and y. So \(D'=(-10,8)\)

• For point E\((10, - 10)\):

After reflection over \(y=x\), we swap x and y. So \(E'=(-10,10)\)

• For point F\((10,0)\):

After reflection over \(y=x\), we swap x and y. So \(F'=(0,10)\)

• For point G\((8,0)\):

After reflection over \(y=x\), we swap x and y. So \(G'=(0,8)\)

Answer:

\(D'(-10, 8)\)
\(E'(-10, 10)\)
\(F'(0, 10)\)
\(G'(0, 8)\)