Skip to content
doubtly
Sign up

Maharashtra SSC Geometry HOTS Questions with Answers – Co-ordinate Geometry | Class 10 Board Exam 2027

Practice set · 1 hr · 55 marks · for SSC 10th and similar exams

2027 60 minutes 55 marks Save WhatsApp

Sections

Most repeated board questions (2024–2026) 11 questions
HOTS: likely questions for 2027 14 questions

About this HOTS set

Here “HOTS” means the important questions most likely to come from Co-ordinate Geometry in the Maharashtra SSC (Class 10) Geometry board exam of 2027. The first section has the board questions that keep repeating; the second has new practice questions in the same board style, including a few harder thinking-type ones on parts of the chapter the board has not asked yet (centroid, trisection, ratio by the X-axis, square/right-triangle proofs).

The board questions in the first section are taken from the official Maharashtra State Board (MSBSHSE) SSC question papers of March 2024, July 2024, March 2025, July 2025, March 2026 and June 2026. All answers and all the new HOTS questions are written by Doubtly. Board MCQs are given with their original four options.

Marks from this chapter in recent board papers

Marks of all questions from this chapter printed in each paper (questions given as internal options are counted too).

Board paperMarks from this chapter
March 20247
July 20249
March 20257
July 20257
March 20267
June 20267

Question types that repeat most

  • Slope from the angle with the X-axis (30° or 45°): in every paper except July 2024.
  • Slope of the line through two points: March 2024, July 2024, July 2025.
  • Collinearity using slopes: March 2024, July 2024, March 2025.
  • Section formula with ratio 2 : 3 (the same question twice) and the midpoint formula: July 2025, March 2026, June 2026.
  • Distance formula, from the origin or between two points: March 2025, June 2026.

Exam tips

  • Write the formula first, then substitute with brackets around negative numbers. The formula line carries marks.
  • For collinearity, state that the point B is common to both lines. Without it the proof is incomplete.
  • Learn \(\tan 30^\circ\), \(\tan 45^\circ\) and \(\tan 60^\circ\) by heart; 1-mark slope questions come every year.
  • For a parallelogram use slopes of opposite sides; for a rhombus/square/right triangle use the distance formula.

Chapters covered

Instructions

Solve on paper with a timer, then check against the solutions.

Most repeated board questions (2024–2026)

  1. Asked in: March 2024, July 2025 and March 2026 board papers

    Angle made by the line with the positive direction of X-axis is 45°. Find the slope of that line.

    1 mark See answer →

  2. Asked in: March 2025 and June 2026 board papers

    Angle made by a line with the positive direction of X-axis is 30°. Find slope of that line.

    1 mark See answer →

  3. Asked in: March 2024 and July 2025 board papers (same type with A(3, 3), B(5, 7) in July 2024)

    Find the slope of the line passing through the points A(2, 3), B(4, 7).

    2 marks See answer →

  4. Asked in: March 2024 and March 2025 board papers (same type with P(–2, 3), Q(1, 2), R(4, 1) in July 2024)

    Determine whether the points are collinear. A(1, –3), B(2, –5), C(–4, 7)

    3 marks See answer →

  5. Asked in: July 2025 and March 2026 board papers

    Find co-ordinates of point P, if P divides the line segment joining the points A(–1, 7) and B(4, –3) in the ratio 2 : 3.

    3 marks See answer →

  6. Asked in: March 2026 board paper (midpoint asked again in July 2025 with P(22, 20), Q(0, 16) and as an activity in June 2026)

    Find the co-ordinates of the midpoint of the line segment joining points P(0, 6) and Q(12, 20).

    2 marks See answer →

  7. Asked in: March 2025 board paper

    Show that points P(1, –2), Q(5, 2), R(3, –1), S(–1, –5) are the vertices of a parallelogram.

    3 marks See answer →

  8. Asked in: June 2026 board paper

    Find the distance between the points P(–1, 1) and Q(5, –7).

    2 marks See answer →

  9. Asked in: July 2024 board paper

    The line \(x - 6y + 11 = 0\) bisects the segment joining the points (8, –1) and (0, k), then find the value of k.

    3 marks See answer →

  10. Asked in: March 2025 board paper

    Distance of point (3, 4) from the origin is ____ .

    1. (A) 7
    2. (B) 1
    3. (C) 5
    4. (D) –5
    1 mark See answer →

  11. Asked in: March 2024 board paper

    Slope of X-axis is ____ .

    1. (A) 1
    2. (B) –1
    3. (C) 0
    4. (D) Cannot be determined
    1 mark See answer →

HOTS: likely questions for 2027

  1. Slope of a line parallel to the Y-axis is ____ .

    1. (A) 0
    2. (B) 1
    3. (C) not defined
    4. (D) –1
    1 mark See answer →

  2. The co-ordinates of the centroid of the triangle with vertices (2, 5), (–1, 4) and (5, 0) are ____ .

    1. (A) (2, 3)
    2. (B) (3, 2)
    3. (C) (6, 9)
    4. (D) (2, 9)
    1 mark See answer →

  3. The distance of the point (–6, 8) from the origin is ____ .

    1. (A) 2
    2. (B) 10
    3. (C) 14
    4. (D) 100
    1 mark See answer →

  4. A line makes an angle of 60° with the positive direction of the X-axis. Find the slope of the line.

    1 mark See answer →

  5. Find the co-ordinates of the midpoint of the segment joining A(–3, 7) and B(5, –1).

    1 mark See answer →

  6. The slope of the line passing through the points (k, 3) and (5, 9) is 2. Find the value of k.

    2 marks See answer →

  7. If the distance between the points (x, 2) and (3, –2) is 5 units, find the possible values of x.

    2 marks See answer →

  8. In what ratio does the point P(2, –5) divide the segment joining A(–3, 5) and B(4, –9)? Complete the following activity.

    Activity: Let P divide AB in the ratio m : n. By section formula, \(x = \dfrac{mx_2 + nx_1}{m + n}\).

    \(\therefore 2 = \dfrac{m(\text{____}) + n(-3)}{m + n}\) \(\therefore 2m + 2n = \text{____}\) \(\therefore \dfrac{m}{n} = \text{____}\)

    Check with the y co-ordinate: \(y = \dfrac{m(-9) + n(5)}{m + n} = \text{____}\)

    3 marks See answer →

  9. Show that the points A(–3, 2), B(1, –2) and C(9, 6) are the vertices of a right-angled triangle. Which angle is the right angle?

    3 marks See answer →

  10. Find the co-ordinates of the points of trisection of the segment joining A(2, –2) and B(–7, 4).

    3 marks See answer →

  11. Two vertices of a triangle are (–2, 5) and (3, 1). If its centroid is G(1, 4), find the third vertex.

    3 marks See answer →

  12. Show that the points A(2, –1), B(5, 3), C(1, 6) and D(–2, 2) are the vertices of a square.

    4 marks See answer →

  13. Points A(1, –1), B(k, 5) and C(7, 8) are collinear.

    (i) Find the value of k using slopes.

    (ii) Find the ratio in which B divides seg AC.

    4 marks See answer →

  14. Find the ratio in which the X-axis divides the segment joining A(–4, 6) and B(8, –3). Also find the co-ordinates of the point of division.

    4 marks See answer →