Question

complete the tables in part a and part b.
part a
indicate whether each point is located in quadrant i, quadrant ii, quadrant iii, quadrant iv, or none of th
point quadrant i quadrant ii quadrant iii quadrant iv none
p(3,4)
r(-3,-4)
s(-3,4)
t(1,-4)
v(3,0)
part b
indicate whether each point is a reflection of p(3,4) across neither axis, across only the y - axis, across o
point across neither axis across only the y - axis across only the x - axis acn

Explanation:

Part A Explanation (for each point, we use the rule of quadrants: Quadrant I: (+, +); Quadrant II: (-, +); Quadrant III: (-, -); Quadrant IV: (+, -); points on axes are "None")

• Point \( P(3, 4) \): \( x = 3>0 \), \( y = 4>0 \), so Quadrant I (already marked correctly).
• Point \( R(-3, -4) \): \( x=-3 < 0 \), \( y = - 4<0 \), so Quadrant III (already marked correctly).
• Point \( S(-3, 4) \): \( x=-3 < 0 \), \( y = 4>0 \), so Quadrant II (already marked correctly).
• Point \( T(3, -4) \): \( x = 3>0 \), \( y=-4 < 0 \), so Quadrant IV (already marked correctly).
• Point \( V(3, 0) \): \( y = 0 \), so it lies on the \( x \)-axis, so "None" (already marked correctly).

Part B (assuming we need to analyze reflections, let's take each point relative to \( P(3,4) \))

• Reflection across \( y \)-axis: changes \( x \) to \( -x \), so the reflection of \( P(3,4) \) across \( y \)-axis is \( (-3,4) \) (which is point \( S \)).
• Reflection across \( x \)-axis: changes \( y \) to \( -y \), so the reflection of \( P(3,4) \) across \( x \)-axis is \( (3,-4) \) (which is point \( T \)).
• Reflection across both axes: changes \( x \) to \( -x \) and \( y \) to \( -y \), so the reflection of \( P(3,4) \) across both axes is \( (-3,-4) \) (which is point \( R \)).
• Point \( P(3,4) \): reflection across neither axis (since it's the original point).
• Point \( V(3,0) \): not a reflection of \( P \) across any axis (since \( y \)-coordinate is 0, not related to reflection of \( P \)'s \( y = 4 \)).

If we need to fill the Part B table (assuming the columns are "Across Neither Axis", "Across Only the \( y \)-axis", "Across Only the \( x \)-axis", "Across Both Axes"):

• Point \( P(3,4) \): Across Neither Axis (mark this).
• Point \( R(-3,-4) \): Across Both Axes (since \( x \) and \( y \) are negated).
• Point \( S(-3,4) \): Across Only the \( y \)-axis (since only \( x \) is negated).
• Point \( T(3,-4) \): Across Only the \( x \)-axis (since only \( y \) is negated).
• Point \( V(3,0) \): Across Neither Axis (not a reflection of \( P \) across any axis).

(Note: Since the Part B table is partially visible, the above is a standard analysis of reflections for the given points relative to \( P(3,4) \).)

If the task was to complete the tables as per the markings, the given Part A table is already correctly marked for each point's quadrant. For Part B, using the reflection rules, we can mark each point's reflection category as above.

Answer:

Part A Explanation (for each point, we use the rule of quadrants: Quadrant I: (+, +); Quadrant II: (-, +); Quadrant III: (-, -); Quadrant IV: (+, -); points on axes are "None")

• Point \( P(3, 4) \): \( x = 3>0 \), \( y = 4>0 \), so Quadrant I (already marked correctly).
• Point \( R(-3, -4) \): \( x=-3 < 0 \), \( y = - 4<0 \), so Quadrant III (already marked correctly).
• Point \( S(-3, 4) \): \( x=-3 < 0 \), \( y = 4>0 \), so Quadrant II (already marked correctly).
• Point \( T(3, -4) \): \( x = 3>0 \), \( y=-4 < 0 \), so Quadrant IV (already marked correctly).
• Point \( V(3, 0) \): \( y = 0 \), so it lies on the \( x \)-axis, so "None" (already marked correctly).

Part B (assuming we need to analyze reflections, let's take each point relative to \( P(3,4) \))

• Reflection across \( y \)-axis: changes \( x \) to \( -x \), so the reflection of \( P(3,4) \) across \( y \)-axis is \( (-3,4) \) (which is point \( S \)).
• Reflection across \( x \)-axis: changes \( y \) to \( -y \), so the reflection of \( P(3,4) \) across \( x \)-axis is \( (3,-4) \) (which is point \( T \)).
• Reflection across both axes: changes \( x \) to \( -x \) and \( y \) to \( -y \), so the reflection of \( P(3,4) \) across both axes is \( (-3,-4) \) (which is point \( R \)).
• Point \( P(3,4) \): reflection across neither axis (since it's the original point).
• Point \( V(3,0) \): not a reflection of \( P \) across any axis (since \( y \)-coordinate is 0, not related to reflection of \( P \)'s \( y = 4 \)).

If we need to fill the Part B table (assuming the columns are "Across Neither Axis", "Across Only the \( y \)-axis", "Across Only the \( x \)-axis", "Across Both Axes"):

• Point \( P(3,4) \): Across Neither Axis (mark this).
• Point \( R(-3,-4) \): Across Both Axes (since \( x \) and \( y \) are negated).
• Point \( S(-3,4) \): Across Only the \( y \)-axis (since only \( x \) is negated).
• Point \( T(3,-4) \): Across Only the \( x \)-axis (since only \( y \) is negated).
• Point \( V(3,0) \): Across Neither Axis (not a reflection of \( P \) across any axis).

(Note: Since the Part B table is partially visible, the above is a standard analysis of reflections for the given points relative to \( P(3,4) \).)

If the task was to complete the tables as per the markings, the given Part A table is already correctly marked for each point's quadrant. For Part B, using the reflection rules, we can mark each point's reflection category as above.