Question

(8,7)
(-3,-2)
(-6,1)
(8,1)
10 (-1,-8) over the y-axis
11 (5,8) over the line y = -x
12 (-5,3) over the x-axis
13 (3,7) over the line y = x (7,3)
14 (-2, -8) over the x-axis (-2,8)

Explanation:

To solve the reflection problems, we use the following rules:

Problem 10: Reflect \((-1, -8)\) over the \(y\)-axis

Step 1: Recall the rule for reflection over the \(y\)-axis

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

Step 2: Apply the rule to \((-1, -8)\)

For the point \((-1, -8)\), \(x = -1\) and \(y = -8\). Applying the rule, we get \((-(-1), -8)=(1, -8)\).

Problem 11: Reflect \((5, 8)\) over the line \(y=-x\)

Step 1: Recall the rule for reflection over \(y = -x\)

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

Step 2: Apply the rule to \((5, 8)\)

For the point \((5, 8)\), \(x = 5\) and \(y = 8\). Applying the rule, we get \((-8, -5)\).

Problem 12: Reflect \((-5, 3)\) over the \(x\)-axis

Step 1: Recall the rule for reflection over the \(x\)-axis

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

Step 2: Apply the rule to \((-5, 3)\)

For the point \((-5, 3)\), \(x=-5\) and \(y = 3\). Applying the rule, we get \((-5, -3)\).

Final Answers:

• Problem 10: \(\boldsymbol{(1, -8)}\)
• Problem 11: \(\boldsymbol{(-8, -5)}\)
• Problem 12: \(\boldsymbol{(-5, -3)}\)

Answer:

To solve the reflection problems, we use the following rules:

Problem 10: Reflect \((-1, -8)\) over the \(y\)-axis

Step 1: Recall the rule for reflection over the \(y\)-axis

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

Step 2: Apply the rule to \((-1, -8)\)

For the point \((-1, -8)\), \(x = -1\) and \(y = -8\). Applying the rule, we get \((-(-1), -8)=(1, -8)\).

Problem 11: Reflect \((5, 8)\) over the line \(y=-x\)

Step 1: Recall the rule for reflection over \(y = -x\)

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

Step 2: Apply the rule to \((5, 8)\)

For the point \((5, 8)\), \(x = 5\) and \(y = 8\). Applying the rule, we get \((-8, -5)\).

Problem 12: Reflect \((-5, 3)\) over the \(x\)-axis

Step 1: Recall the rule for reflection over the \(x\)-axis

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

Step 2: Apply the rule to \((-5, 3)\)

For the point \((-5, 3)\), \(x=-5\) and \(y = 3\). Applying the rule, we get \((-5, -3)\).

Final Answers:

• Problem 10: \(\boldsymbol{(1, -8)}\)
• Problem 11: \(\boldsymbol{(-8, -5)}\)
• Problem 12: \(\boldsymbol{(-5, -3)}\)