Question 1: Find the negative reciprocal of the line with gradient 3/4.

Answer: -4/3

Question 2: Calculate the gradient of a line perpendicular to one with gradient -2.

Answer: 1/2

Question 3: Determine the negative reciprocal of y = -5x + 2.

Answer: 1/5

Question 4: Plot the graph of y = 2x and its perpendicular line passing through the origin.

Answer: Student draws the line with gradient -1/2 passing through (0,0).

Question 5: Construct a line perpendicular to y = -3x + 4 that passes through the point (2, 3).

Answer: Line with gradient 1/3 passing through (2,3).

Question 6: A line has a gradient of 7. What is the gradient of the line perpendicular to it?

Answer: -1/7

Question 7: Given the equation y = (2/5)x + 1, find the equation of the line perpendicular to it passing through (0, 0).

Answer: y = -5/2 x

Question 8: Explain why the slopes 2/3 and -3/2 are negative reciprocals and what this implies about their lines.

Answer: Because 2/3 and -3/2 are negative reciprocals, their product is -1, implying the lines are perpendicular.

Question 9: If a line is perpendicular to y = 4x + 1, what is its equation passing through the point (1, 2)?

Answer: y - 2 = -1/4(x - 1)

Question 10: A student mistakenly thinks the negative reciprocal of y = 1/3 x is 3. Identify and correct this mistake.

Answer: The correct negative reciprocal of 1/3 is -3, not 3.

Question 11: A line has a gradient of -2/5. Find the equation of a perpendicular line passing through the point (4, -1).

Answer: y + 1 = 5/2(x - 4)