Question

list the coordinates of the figure. then list the coordinates after a reflection over the x-axis.
grid image with points r, b, y
r: b: y:
r: b: y:
list the coordinates of the figure. then list the coordinates after a reflection over the y-axis.
grid image with points r, b, y
r: b: y:
r: b: y:

Explanation:

Left Figure (Reflection over x - axis)

Step 1: Determine original coordinates

• For point \(R\): Looking at the grid, it is at the origin of the local coordinate system we can assume, so \(R=(0,0)\).
• For point \(B\): By counting the grid squares, if we consider the x - coordinate (horizontal) and y - coordinate (vertical), let's say each grid square is 1 unit. If we move right 8 units and up 8 units from the origin (where \(R\) is), \(B=(8,8)\).
• For point \(Y\): Moving right 6 units and up 1 unit from the origin, \(Y=(6,1)\).

Step 2: Apply reflection over x - axis rule

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

• For \(R=(0,0)\), applying the rule: \(R'=(0,- 0)=(0,0)\)
• For \(B=(8,8)\), applying the rule: \(B'=(8,-8)\)
• For \(Y=(6,1)\), applying the rule: \(Y'=(6,-1)\)

Right Figure (Reflection over y - axis)

Step 1: Determine original coordinates

• For point \(R\): By counting the grid squares, if we assume the vertical line (y - axis) and horizontal line (x - axis), let's say moving right 4 units and up 1 unit from the y - axis (we can set the y - axis as a reference). So \(R=(4,1)\).
• For point \(B\): Moving left 4 units (since it's to the left of the y - axis? Wait, no, looking at the grid, if the y - axis is the middle vertical line, let's re - evaluate. Let's assume the y - axis is at \(x = 0\). If we count the units, for \(B\): moving left 4 units (x=- 4) and up 8 units (y = 8), so \(B=(-4,8)\).
• For point \(Y\): Moving left 8 units (x=-8) and up 0 units (y = 0), so \(Y=(-8,0)\).

Step 2: Apply reflection over y - axis rule

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

• For \(R=(4,1)\), applying the rule: \(R'=(-4,1)\)
• For \(B=(-4,8)\), applying the rule: \(B'=(4,8)\)
• For \(Y=(-8,0)\), applying the rule: \(Y'=(8,0)\)

Final Answers (Filling the tables)

Left Table (Reflection over x - axis)

\(R\)	\(B\)	\(Y\)

\(R'\)	\(B'\)	\(Y'\)

Right Table (Reflection over y - axis)

\(R\)	\(B\)	\(Y\)

\(R'\)	\(B'\)	\(Y'\)

Answer:

Left Figure (Reflection over x - axis)

Step 1: Determine original coordinates

• For point \(R\): Looking at the grid, it is at the origin of the local coordinate system we can assume, so \(R=(0,0)\).
• For point \(B\): By counting the grid squares, if we consider the x - coordinate (horizontal) and y - coordinate (vertical), let's say each grid square is 1 unit. If we move right 8 units and up 8 units from the origin (where \(R\) is), \(B=(8,8)\).
• For point \(Y\): Moving right 6 units and up 1 unit from the origin, \(Y=(6,1)\).

Step 2: Apply reflection over x - axis rule

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

• For \(R=(0,0)\), applying the rule: \(R'=(0,- 0)=(0,0)\)
• For \(B=(8,8)\), applying the rule: \(B'=(8,-8)\)
• For \(Y=(6,1)\), applying the rule: \(Y'=(6,-1)\)

Right Figure (Reflection over y - axis)

Step 1: Determine original coordinates

• For point \(R\): By counting the grid squares, if we assume the vertical line (y - axis) and horizontal line (x - axis), let's say moving right 4 units and up 1 unit from the y - axis (we can set the y - axis as a reference). So \(R=(4,1)\).
• For point \(B\): Moving left 4 units (since it's to the left of the y - axis? Wait, no, looking at the grid, if the y - axis is the middle vertical line, let's re - evaluate. Let's assume the y - axis is at \(x = 0\). If we count the units, for \(B\): moving left 4 units (x=- 4) and up 8 units (y = 8), so \(B=(-4,8)\).
• For point \(Y\): Moving left 8 units (x=-8) and up 0 units (y = 0), so \(Y=(-8,0)\).

Step 2: Apply reflection over y - axis rule

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

• For \(R=(4,1)\), applying the rule: \(R'=(-4,1)\)
• For \(B=(-4,8)\), applying the rule: \(B'=(4,8)\)
• For \(Y=(-8,0)\), applying the rule: \(Y'=(8,0)\)

Final Answers (Filling the tables)

Left Table (Reflection over x - axis)

\(R\)	\(B\)	\(Y\)

\(R'\)	\(B'\)	\(Y'\)

Right Table (Reflection over y - axis)

\(R\)	\(B\)	\(Y\)

\(R'\)	\(B'\)	\(Y'\)