Question

plot all of the points of the reflected figure. you may click a plotted point to delete it.

Explanation:

Answer:

To solve the reflection of the given figure (assuming reflection over the \( y \)-axis, common in such problems), follow these steps for each vertex:

Step 1: Identify Original Points

First, determine the coordinates of the original vertices. Let's assume the original points (from the graph) are:

• Point 1: \( (-8, -2) \)
• Point 2: \( (-5, -7) \)
• Point 3: \( (-3, -9) \)
• Point 4: \( (-1, -9) \) (Wait, actually, looking at the graph, let's re - identify. Let's get the correct coordinates by looking at the grid. Let's say the original triangle (or quadrilateral) has vertices:

Let's take the left - most point: \( (-8, -2) \), then a point at \( (-5, -7) \), then \( (-3, -9) \), and \( (-1, -9) \)? Wait, maybe it's a triangle. Wait, the graph shows a pink figure with three or four vertices. Let's correctly identify the coordinates:

Looking at the \( x \)-axis (horizontal) and \( y \)-axis (vertical). Each grid square is 1 unit.

Let's list the original vertices:

1. Let's say the top - most (left - most) vertex: \( x=-8 \), \( y = - 2 \), so \( (-8,-2) \)
2. Then a vertex: \( x=-5 \), \( y=-7 \), so \( (-5,-7) \)
3. Then a vertex: \( x=-3 \), \( y = - 9 \), so \( (-3,-9) \)
4. Then a vertex: \( x=-1 \), \( y=-9 \), so \( (-1,-9) \) (maybe a quadrilateral)

Step 2: Apply Reflection over \( y \)-axis

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

• For point \( (-8,-2) \):

Using the reflection rule \( (x,y)\to(-x,y) \), substitute \( x = - 8 \) and \( y=-2 \). We get \( (8,-2) \)

• For point \( (-5,-7) \):

Substitute \( x=-5 \) and \( y = - 7 \) into the rule \( (x,y)\to(-x,y) \). We get \( (5,-7) \)

• For point \( (-3,-9) \):

Substitute \( x=-3 \) and \( y=-9 \) into the rule. We get \( (3,-9) \)

• For point \( (-1,-9) \):

Substitute \( x=-1 \) and \( y=-9 \) into the rule. We get \( (1,-9) \)

Step 3: Plot the Reflected Points

Now, plot the points \( (8,-2) \), \( (5,-7) \), \( (3,-9) \), and \( (1,-9) \) on the coordinate plane.

If the reflection is over the \( x \)-axis, the rule is \( (x,y)\to(x, - y) \). But since the original figure is below the \( x \)-axis ( \( y \)-values negative), reflection over \( y \)-axis is more likely (to get a figure on the right side).

If we assume reflection over \( x \)-axis:

• For point \( (-8,-2) \), reflected point is \( (-8,2) \)
• For point \( (-5,-7) \), reflected point is \( (-5,7) \)
• For point \( (-3,-9) \), reflected point is \( (-3,9) \)
• For point \( (-1,-9) \), reflected point is \( (-1,9) \)

But since the problem says "reflect the fig" (probably "reflect the figure"), and without more information, the most common reflection in such grid problems is over the \( y \)-axis.

So the reflected points (for \( y \)-axis reflection) are \( (8,-2) \), \( (5,-7) \), \( (3,-9) \), \( (1,-9) \). Plot these points on the given grid (the right - hand side of the \( y \)-axis with the same \( y \)-coordinates and \( x \)-coordinates as the negatives of the original \( x \)-coordinates).