Question

1. reflection across y-axis

Explanation:

Step1: Identify coordinates of points

Let's assume the grid has each square with side length 1. Let's find coordinates of points \( U \), \( L \), and \( X \) (let's correct the label, probably a typo, let's say the top - right point is \( X \) with original coordinates. Let's find:

• Point \( U \): Let's say from the grid, if we consider the y - axis, let's assume the x - coordinate of \( U \) is \( x=-3 \), y - coordinate \( y = 4 \) (so \( U(-3,4) \))
• Point \( L \): x - coordinate \( x=-3 \), y - coordinate \( y = 1 \) (so \( L(-3,1) \))
• Point \( X \): x - coordinate \( x = 0 \), y - coordinate \( y = 4 \) (so \( X(0,4) \))

Step2: Apply reflection over y - axis rule

The rule for reflection over the y - axis is \((x,y)\to(-x,y)\)

• For point \( U(-3,4) \):

Applying the rule, \( x=-3\), so \(-x = 3\), \( y = 4\). So the reflected point \( U'=(3,4) \)

• For point \( L(-3,1) \):

Applying the rule, \( x=-3\), so \(-x = 3\), \( y = 1\). So the reflected point \( L'=(3,1) \)

• For point \( X(0,4) \):

Applying the rule, \( x = 0\), so \(-x=0\), \( y = 4\). So the reflected point \( X'=(0,4) \)

Step3: Plot the reflected points

Plot \( U'(3,4) \), \( L'(3,1) \), and \( X'(0,4) \) on the grid and connect them to get the reflected figure.

Answer:

To reflect the figure across the \( y \) - axis, we use the reflection rule \((x,y)\to(-x,y)\). For the given points (assuming \( U(-3,4) \), \( L(-3,1) \), \( X(0,4) \)):

• \( U \) reflects to \( (3,4) \)
• \( L \) reflects to \( (3,1) \)
• \( X \) reflects to \( (0,4) \)

Plot these new points and connect them to obtain the reflected figure.