Question

18
identify the x- or y-axis as the line of reflection when two ordered pairs have an opposite x- or y-coordinate (l4)

point r has the coordinates (-2, -5).

• what will be the new coordinates of point r if it reflects over the x-axis?
• which coordinates are the same?
• which coordinates are the opposite?

point c has the coordinates (7, -1).

• what will be the new coordinates of point c if it reflects over the y-axis?
• which coordinates are the same?
• which coordinates are the opposite?

point l has the coordinates (-4, -3).

• what will be the new coordinates of point l if it reflects over the y-axis?
• which coordinates are the same?
• which coordinates are the opposite?

point j has the coordinates (6, 7).

• what will be the new coordinates of point j if it reflects over the x-axis?
• which coordinates are the same?
• which coordinates are the opposite?

Explanation:

Point R (-2, -5) reflecting over x - axis:

Step 1: Recall reflection over x - axis rule

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

Step 2: Apply the rule to Point R

For point \(R(-2,-5)\), \(x=-2\) and \(y = - 5\). After reflection over x - axis, the new point \(R'\) has coordinates \((-2,5)\).

Step 3: Identify same and opposite coordinates

• Same coordinates: The x - coordinate (\(-2\)) is the same.
• Opposite coordinates: The y - coordinate (\(-5\) and \(5\) are opposites).

Point L (-4, -3) reflecting over y - axis:

Step 1: Recall reflection over y - axis rule

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

Step 2: Apply the rule to Point L

For point \(L(-4,-3)\), \(x = - 4\) and \(y=-3\). After reflection over y - axis, the new point \(L'\) has coordinates \((4,-3)\).

Step 3: Identify same and opposite coordinates

• Same coordinates: The y - coordinate (\(-3\)) is the same.
• Opposite coordinates: The x - coordinate (\(-4\) and \(4\) are opposites).

Point C (7, -1) reflecting over y - axis:

Step 1: Recall reflection over y - axis rule

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

Step 2: Apply the rule to Point C

For point \(C(7,-1)\), \(x = 7\) and \(y=-1\). After reflection over y - axis, the new point \(C'\) has coordinates \((-7,-1)\).

Step 3: Identify same and opposite coordinates

• Same coordinates: The y - coordinate (\(-1\)) is the same.
• Opposite coordinates: The x - coordinate (\(7\) and \(-7\) are opposites).

Point J (6,7) reflecting over x - axis:

Step 1: Recall reflection over x - axis rule

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

Step 2: Apply the rule to Point J

For point \(J(6,7)\), \(x = 6\) and \(y = 7\). After reflection over x - axis, the new point \(J'\) has coordinates \((6,-7)\).

Step 3: Identify same and opposite coordinates

• Same coordinates: The x - coordinate (\(6\)) is the same.
• Opposite coordinates: The y - coordinate (\(7\) and \(-7\) are opposites).

Answer:

• Point R reflection over x - axis: \(R'(-2,5)\), same: x - coordinate, opposite: y - coordinate.
• Point L reflection over y - axis: \(L'(4,-3)\), same: y - coordinate, opposite: x - coordinate.
• Point C reflection over y - axis: \(C'(-7,-1)\), same: y - coordinate, opposite: x - coordinate.
• Point J reflection over x - axis: \(J'(6,-7)\), same: x - coordinate, opposite: y - coordinate.