1. write the algebraic rule for the transformation shown
rule:
why is this a translation/rotation/reflection?
how does my rule match what i see on the graph?
2. write the algebraic rule for the transformation shown
rule:
why is this a translation/rotation/reflection?
how does my rule match what i see on the graph?
3. write the algebraic rule for the transformation shown
rule:
why is this a translation/rotation/reflection?
how does my rule match what i see on the graph?
4. write the algebraic rule for the transformation shown
rule:
why is this a translation/rotation/reflection?
how does my rule match what i see on the graph?
5. the arrows below show that the coordinates on the left are mapped to the coordinates on the right. fill in the blanks to give the coordinates after the reflection.
(a) original coordinates → final coordinates
a (-8, -3) → a (_,_)
b (-4, -3) → b (_,_)
c (-2, 5) → c (_,_)
(b) choose the general rule below that describes the reflection mapping △abc to △abc
(x,y)→(-x,-y) (x,y)→(-y,-x)
(x,y)→(-y,x) (x,y)→(-x,y)
(x,y)→(y,x) (x,y)→(x,-y)
(x,y)→(y,-x)

Question

Accepted Answer

### 1.
# Explanation:
## Step1: Identify the transformation type
The figure $A$ and $A'$ are symmetric about the $x -$axis. For a reflection over the $x -$axis, the rule is $(x,y)\to(x, - y)$.
## Step2: Verify the rule
Take a point on $A$, say $(0,2)$. Applying the rule $(0,2)\to(0,- 2)$, which is a point on $A'$.

# Answer:
Rule: $(x,y)\to(x, - y)$. This is a reflection because the figure is flipped over the $x -$axis. The rule matches the graph as each $y -$coordinate of points on $A$ changes its sign to get the corresponding points on $A'$.

### 2.
# Explanation:
## Step1: Identify the transformation type
The figure $A$ and $A'$ are symmetric about the origin. For a rotation of $180^{\circ}$ about the origin (which is equivalent to the transformation $(x,y)\to(-x,-y)$).
## Step2: Verify the rule
Take a point on $A$, say $(-4,2)$. Applying the rule $(-4,2)\to(4,-2)$, which is a point on $A'$.

# Answer:
Rule: $(x,y)\to(-x,-y)$. This is a rotation (or reflection through the origin)  because the figure is turned $180^{\circ}$ about the origin. The rule matches the graph as each $x$ and $y$ coordinates of points on $A$ change their signs to get the corresponding points on $A'$.

### 3.
# Explanation:
## Step1: Identify the transformation type
The figure is symmetric about the $y -$axis. For a reflection over the $y -$axis, the rule is $(x,y)\to(-x,y)$.
## Step2: Verify the rule
Take a point on the left - hand triangle, say $(-2,-4)$. Applying the rule $(-2,-4)\to(2,-4)$, which is a point on the right - hand triangle.

# Answer:
Rule: $(x,y)\to(-x,y)$. This is a reflection because the figure is flipped over the $y -$axis. The rule matches the graph as each $x -$coordinate of points on one triangle changes its sign to get the corresponding points on the other triangle.

### 4.
# Explanation:
## Step1: Identify the transformation type
The figure is a rotation. If we consider the general rotation formula. For a rotation of $90^{\circ}$ clockwise about the origin, the rule is $(x,y)\to(y,-x)$.
## Step2: Verify the rule
Take a vertex of the left - hand triangle, say $(-4,4)$. Applying the rule $(-4,4)\to(4,4)$ (incorrect, let's re - check). Wait, for a rotation of $90^{\circ}$ counter - clockwise about the origin, the rule is $(x,y)\to(-y,x)$. Take a point $(-4,4)$ on the left - hand triangle, applying $(x,y)\to(-y,x)$ gives $(-4,4)\to(-4,-4)$ (no). Wait, actually, if we consider the transformation: take a point $(-4,4)$ on the left - hand figure and a corresponding point $(4,4)$ on the right - hand figure (incorrect). Wait, using the property of rotation. Let's take a point $(-2,4)$ on the left - hand figure. If we assume a rotation of $90^{\circ}$ clockwise about the origin $(x,y)\to(y, - x)$, $(-2,4)\to(4,2)$ (matches).

# Answer:
Rule: $(x,y)\to(y,-x)$. This is a rotation because the figure is turned $90^{\circ}$ about the origin. The rule matches the graph as for each point $(x,y)$ on the original figure,  the new $x$ - coordinate is the old $y$ - coordinate and the new $y$ - coordinate is the negative of the old $x$ - coordinate.

### 5.
# Explanation:
## Part (a)
For a reflection over the $y -$axis, the rule is $(x,y)\to(-x,y)$.
- For $A(-8,-3)$, applying the rule $(x,y)\to(-x,y)$ gives $A'(8,-3)$.
- For $B(-4,-3)$, applying the rule $(x,y)\to(-x,y)$ gives $B'(4,-3)$.
- For $C(-2,5)$, applying the rule $(x,y)\to(-x,y)$ gives $C'(2,5)$.

## Part (b)
The general rule for reflection over the $y -$axis is $(x,y)\to(-x,y)$.

# Answer:
(a) $A'(8,-3)$, $B'(4,-3)$, $C'(2,5)$
(b) $(x,y)\to(-x,y)$

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QUESTION IMAGE

Question

Explanation:

1.

Step1: Identify the transformation type

Step2: Verify the rule

Step1: Identify the transformation type

Step2: Verify the rule

Step1: Identify the transformation type

Step2: Verify the rule

Answer:

2.