Question

1. plot and label each point on the coordinate plane based on the characteristics described.

a. plot point b with an x - coordinate of 0.

b. plot point g with a y - coordinate of 0.

c. plot point t in quadrant ii with an x - coordinate of - 3.

d. plot point c in quadrant iii with a y - coordinate of - 4.

e. plot point m in quadrant i with a y - coordinate of 2.

f. plot point w in quadrant iv with an x - coordinate of 1.

Explanation:

Part a: Plot Point B

• A point with an \( x \)-coordinate of 0 lies on the \( y \)-axis. The coordinates of point \( B \) can be written as \( (0, y) \), where \( y \) can be any real number (we can choose a value, say \( y = 3 \) for plotting, so \( B=(0, 3) \)). To plot, find the intersection of \( x = 0 \) (the \( y \)-axis) and the chosen \( y \)-value.

Part b: Plot Point G

• A point with a \( y \)-coordinate of 0 lies on the \( x \)-axis. The coordinates of point \( G \) can be written as \( (x, 0) \), where \( x \) can be any real number (we can choose \( x = 2 \) for plotting, so \( G=(2, 0) \)). To plot, find the intersection of \( y = 0 \) (the \( x \)-axis) and the chosen \( x \)-value.

Part c: Plot Point T

• In quadrant II, the \( x \)-coordinate is negative and the \( y \)-coordinate is positive. Given \( x=-3 \), let's choose \( y = 4 \) (any positive number). So the coordinates of \( T \) are \( (-3, 4) \). To plot, move 3 units left on the \( x \)-axis (since \( x=-3 \)) and 4 units up on the \( y \)-axis (since \( y = 4 \)).

Part d: Plot Point C

Answer:

• In quadrant IV, the \( x \)-coordinate is positive and the \( y \)-coordinate is negative. Given \( x = 1 \), let's choose \( y=-2 \) (any negative number). So the coordinates of \( W \) are \( (1, -2) \). To plot, move 1 unit right on the \( x \)-axis (since \( x = 1 \)) and 2 units down on the \( y \)-axis (since \( y=-2 \)).

Final Plotting Summary (Coordinates Chosen for Plotting):

• \( B=(0, 3) \) (on \( y \)-axis)
• \( G=(2, 0) \) (on \( x \)-axis)
• \( T=(-3, 4) \) (quadrant II)
• \( C=(-2, -4) \) (quadrant III)
• \( M=(3, 2) \) (quadrant I)
• \( W=(1, -2) \) (quadrant IV)

To plot these points:

• For \( B \): Find \( x = 0 \) (the \( y \)-axis) and mark at \( y = 3 \).
• For \( G \): Find \( y = 0 \) (the \( x \)-axis) and mark at \( x = 2 \).
• For \( T \): Move 3 units left from the origin (since \( x=-3 \)) and 4 units up (since \( y = 4 \)) in quadrant II.
• For \( C \): Move 2 units left from the origin (since \( x=-2 \)) and 4 units down (since \( y=-4 \)) in quadrant III.
• For \( M \): Move 3 units right from the origin (since \( x = 3 \)) and 2 units up (since \( y = 2 \)) in quadrant I.
• For \( W \): Move 1 unit right from the origin (since \( x = 1 \)) and 2 units down (since \( y=-2 \)) in quadrant IV.