Question

1. here is a list of points

a=(0.5,4) b=(-4,5) c=(7,-2) d=(6,0) e=(0,-3)
on the coordinate plane:
a. plot each point and label each with its coordinates.
b. using the x - axis as the line of reflection, plot the image of each point.
c. label the image of each point with its coordinates.
d. include a label using a letter. for example, the image of point a should be labeled a.

Explanation:

Step1: Recall coordinate - plane plotting rules

To plot a point $(x,y)$ on the coordinate - plane, $x$ is the horizontal displacement and $y$ is the vertical displacement from the origin $(0,0)$.

Step2: Recall reflection rule over x - axis

When a point $(x,y)$ is reflected over the $x$ - axis, the new point is $(x, - y)$.

Step3: Plot original points

• Point $A=(0.5,4)$: Move 0.5 units to the right along the $x$ - axis and 4 units up along the $y$ - axis and label it $A$.
• Point $B = (-4,5)$: Move 4 units to the left along the $x$ - axis and 5 units up along the $y$ - axis and label it $B$.
• Point $C=(7,-2)$: Move 7 units to the right along the $x$ - axis and 2 units down along the $y$ - axis and label it $C$.
• Point $D=(6,0)$: Move 6 units to the right along the $x$ - axis (since $y = 0$, it lies on the $x$ - axis) and label it $D$.
• Point $E=(0,-3)$: Since $x = 0$, it lies on the $y$ - axis. Move 3 units down along the $y$ - axis and label it $E$.

Step4: Find and plot reflected points

• For point $A=(0.5,4)$, its reflection $A'=(0.5,-4)$. Plot $A'$ by moving 0.5 units to the right along the $x$ - axis and 4 units down along the $y$ - axis.
• For point $B=(-4,5)$, its reflection $B'=(-4,-5)$. Plot $B'$ by moving 4 units to the left along the $x$ - axis and 5 units down along the $y$ - axis.
• For point $C=(7,-2)$, its reflection $C'=(7,2)$. Plot $C'$ by moving 7 units to the right along the $x$ - axis and 2 units up along the $y$ - axis.
• For point $D=(6,0)$, its reflection $D'=(6,0)$ (since the point lies on the $x$ - axis, its reflection is itself).
• For point $E=(0,-3)$, its reflection $E'=(0,3)$. Plot $E'$ by moving 3 units up along the $y$ - axis.

Answer:

The original points $A=(0.5,4)$, $B = (-4,5)$, $C=(7,-2)$, $D=(6,0)$, $E=(0,-3)$ are plotted as described. The reflected points are $A'=(0.5,-4)$, $B'=(-4,-5)$, $C'=(7,2)$, $D'=(6,0)$, $E'=(0,3)$ and are also plotted and labeled as required.