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

Answer: (3, 4)

Question 2: Plot the point (-2, 5). Then, plot the point (2, -3).

Answer: Points plotted at (-2, 5) and (2, -3).

Question 3: Determine the coordinates of the point that is 4 units to the right and 2 units up from (0, 0).

Answer: (4, 2)

Question 4: Plot the point (−5, −3). Then, identify its quadrant.

Answer: Quadrant III

Question 5: Plot the points (1, 2), (3, 4), and (5, 6). Connect them to form a line. What is the slope of this line?

Answer: Slope = (6−2)/(5−3) = 4/2 = 2

Question 6: A map shows the coordinates of a park entrance at (2, 3) and the playground at (8, 7). Plot both points and find the distance between them.

Answer: Distance = √[(8−2)² + (7−3)²] = √(36 + 16) = √52 ≈ 7.21 units

Question 7: Plot the points (−1, 0) and (0, −1). What is the change in x and y between these points?

Answer: Δx = 1, Δy = -1

Question 8: Construct a triangle with vertices at (0, 0), (4, 0), and (0, 3). What is the length of the hypotenuse?

Answer: Hypotenuse = √(4² + 3²) = √(16 + 9) = √25 = 5

Question 9: Plot the point (2, -4). Then, reflect it across the x-axis. What are the new coordinates?

Answer: (2, 4)

Question 10: Plot the point (7, 2) and the point (7, -3). What geometric shape do these points form?

Answer: A vertical line segment

Question 11: Identify and correct the mistake in plotting the point (−3, 4) when a student places it at (4, −3).

Answer: The student swapped the x and y coordinates; correct position is (−3, 4).