Question

part d
a translation 2 units right, then a reflection across ( x = 0 ).
q: (\\(quad\\))

Explanation:

To solve this, we need the original coordinates of point \( Q \). Since they are not provided, we'll assume a general point \( Q=(x,y) \) and apply the transformations.

Step 1: Translation 2 units right

A translation 2 units right changes the \( x \)-coordinate by adding 2. So, the new coordinates after translation are \( (x + 2,y) \).

Step 2: Reflection across \( x = 0 \) (the \( y \)-axis)

The rule for reflecting a point \( (a,b) \) across the \( y \)-axis is \( (a,b)\to(-a,b) \). Applying this to the point \( (x + 2,y) \), we get \( (- (x + 2),y)=(-x - 2,y) \).

If we assume the original point \( Q \) (for example, if \( Q=(0,0) \)):

• After translation 2 units right: \( (0 + 2,0)=(2,0) \)
• After reflection across \( x = 0 \): \( (-2,0) \)

But since the original coordinates of \( Q \) are not given, we need that information. If we suppose the original \( Q \) is, say, \( (x,y) \), the final \( Q' \) would be \( (-x - 2,y) \).

If we take a common example, let's say \( Q=(1,1) \):

• Translation 2 units right: \( (1 + 2,1)=(3,1) \)
• Reflection across \( x = 0 \): \( (-3,1) \)

However, without the original coordinates of \( Q \), we can't give a specific numerical answer. Please provide the original coordinates of point \( Q \) to get the exact \( Q' \).

Answer:

To solve this, we need the original coordinates of point \( Q \). Since they are not provided, we'll assume a general point \( Q=(x,y) \) and apply the transformations.

Step 1: Translation 2 units right

A translation 2 units right changes the \( x \)-coordinate by adding 2. So, the new coordinates after translation are \( (x + 2,y) \).

Step 2: Reflection across \( x = 0 \) (the \( y \)-axis)

The rule for reflecting a point \( (a,b) \) across the \( y \)-axis is \( (a,b)\to(-a,b) \). Applying this to the point \( (x + 2,y) \), we get \( (- (x + 2),y)=(-x - 2,y) \).

If we assume the original point \( Q \) (for example, if \( Q=(0,0) \)):

• After translation 2 units right: \( (0 + 2,0)=(2,0) \)
• After reflection across \( x = 0 \): \( (-2,0) \)

But since the original coordinates of \( Q \) are not given, we need that information. If we suppose the original \( Q \) is, say, \( (x,y) \), the final \( Q' \) would be \( (-x - 2,y) \).

If we take a common example, let's say \( Q=(1,1) \):

• Translation 2 units right: \( (1 + 2,1)=(3,1) \)
• Reflection across \( x = 0 \): \( (-3,1) \)

However, without the original coordinates of \( Q \), we can't give a specific numerical answer. Please provide the original coordinates of point \( Q \) to get the exact \( Q' \).