Exam Questions & Step-by-Step Markschemes (7 Problems)
Question 1 • 2024
3 Marks
Find the equation of the perpendicular bisector of the line segment joining the points A(3, -2) and B(-1, 4) .
Answer: 2x - 3y + 1 = 0
Question 2 • 2024
4 Marks
Find the ratio in which the line segment joining the points A(-3, 10) and B(6, -8) is divided by the point P(-1, 6) . Also verify the coordinate using the y -value.
Answer: \text{Ratio} = 2 : 7
Question 3 • 2023
4 Marks
The line segment joining P(3, 3) and Q(6, -6) is intersected by x -axis at A . Find: (i) Ratio in which A divides PQ . (ii) Coordinates of A . (iii) Equation of line through A perpendicular to PQ .
Answer: (i) \ 1 : 2 \quad (ii) \ A(4, 0) \quad (iii) \ x - 3y - 4 = 0
Question 4 • 2023
4 Marks
Point P(2, -4) is reflected in the x -axis to point P' . Point P' is then reflected in the origin to point P'' . (i) Write down the coordinates of P' and P'' . (ii) Find the length of the segment PP'' . (iii) Write down the single transformation that maps P directly to P'' .
Answer: (i) \ P'(2, 4), \; P''(-2, -4) \quad (ii) \ 4 \text{ units} \quad (iii) \ \text{Reflection in the } y\text{-axis}
Question 5 • 2023
4 Marks
Find the equation of the perpendicular bisector of the line segment joining the points A(4, 2) and B(-2, 6) .
Answer: 3x - 2y + 5 = 0
Question 6 • 2024
3 Marks
The line segment joining P(3, 3) and Q(6, -6) is trisected by points A and B , where A is nearer to P . If A lies on the line 2x + y + k = 0 , find the value of k .
Answer: k = -8