Question 1: Plot the point (3, 4) on the grid. What are the coordinates of this point?

Answer: (3, 4)

Question 2: Plot the points (−2, 3), (0, 0), and (4, −1). Which point is closest to the origin?

Answer: (0, 0)

Question 3: Calculate the distance between points (1, 2) and (4, 6). Use the distance formula: √[(x₂−x₁)² + (y₂−y₁)²]

Answer: 5

Question 4: Plot the point that is 3 units to the right and 2 units up from the origin.

Answer: (3, 2)

Question 5: Construct a triangle with vertices at (1, 1), (4, 1), and (2, 4). What are the lengths of the sides?

Answer: 3, 3, and approximately 3.6

Question 6: Plot the points (−1, −2), (2, −3), and (0, 0). Connect them to form a triangle. Which side is the longest?

Answer: Side between (−1, −2) and (2, −3), approximately 3.16 units

Question 7: Find the midpoint of the segment joining (2, 5) and (6, 1).

Answer: (4, 3)

Question 8: If a point is at (x, y) and the point (x + 2, y − 3) is plotted, what is the horizontal and vertical change?

Answer: Horizontal change: 2; Vertical change: -3

Question 9: Plot the point (−3, 4) and reflect it across the y-axis. What are the coordinates of the reflected point?

Answer: (3, 4)

Question 10: Identify and correct the mistake in plotting the point (5, −3) if a student accidentally plotted it at (−5, 3).

Answer: The correct point is (5, −3). The mistake was reflecting the signs of the coordinates.

Question 11: Plot the point (1, 1). Then, plot the point that is 4 units left and 3 units down from it. What are the coordinates of this second point?

Answer: (-3, -2)