Introduction to Coordinate Geometry

Maths, SSC-KPK Class 9. This chapter is split into 9 topics and has 241 practice questions. The topics covered are listed below, followed by 10 free sample questions from the chapter.

Topics in this chapter

1. Collinear and non-collinear points 29 questions
2. Quadrilaterals from four points: square, rectangle, parallelogram 30 questions
3. Unit 9 review exercise and summary 22 questions
4. The distance formula and its derivation (Part 1) 25 questions
5. Standard results proved by coordinate geometry 22 questions
6. The midpoint formula 30 questions
7. Triangles from three points: equilateral, isosceles, scalene, right-angled 30 questions
8. The distance formula and its derivation (Part 2) 24 questions
9. Coordinate geometry: introduction and distance on the real line 29 questions

Sample questions: Introduction to Coordinate Geometry

10 sample questions with the correct answer and an explanation. Try to answer each one before reading the explanation.

Q1. The points A(0, 0), B(1, 4), C(4, 2) and D(3, −2) are the vertices of

• A. a square
• B. a rectangle (not a square)
• C. a rhombus (not a square)
• D. a parallelogram (not a rectangle)(correct answer)

Answer: D.Using the distance formula: |AB| = √17, |BC| = √13, |CD| = √17, |DA| = √13, |AC| = √20, |BD| = √40; this gives a parallelogram (not a rectangle).

Q2. The points A(−2, 0), B(6, 0), C(6, 6) and D(−2, 6) are the vertices of

• A. a parallelogram (not a rectangle)
• B. a square
• C. a rectangle (not a square)(correct answer)
• D. a rhombus (not a square)

Answer: C.Using the distance formula: |AB| = √64, |BC| = √36, |CD| = √64, |DA| = √36, |AC| = √100, |BD| = √100; this gives a rectangle (not a square).

Q3. The points A(0, 0), B(4, 0), C(5, 3) and D(1, 3) are the vertices of

• A. a parallelogram (not a rectangle)(correct answer)
• B. a square
• C. a rectangle (not a square)
• D. a rhombus (not a square)

Answer: A.Using the distance formula: |AB| = √16, |BC| = √10, |CD| = √16, |DA| = √10, |AC| = √34, |BD| = √18; this gives a parallelogram (not a rectangle).

Q4. The points A(2, 0), B(5, 0), C(5, 4) and D(2, 4) are the vertices of

• A. a parallelogram (not a rectangle)
• B. a rectangle (not a square)(correct answer)
• C. a square
• D. a rhombus (not a square)

Answer: B.Using the distance formula: |AB| = √9, |BC| = √16, |CD| = √9, |DA| = √16, |AC| = √25, |BD| = √25; this gives a rectangle (not a square).

Q5. The points A(−4, −1), B(1, 0), C(7, −3) and D(2, −4) are the vertices of

• A. a rectangle (not a square)
• B. a rhombus (not a square)
• C. a parallelogram (not a rectangle)(correct answer)
• D. a square

Answer: C.Using the distance formula: |AB| = √26, |BC| = √45, |CD| = √26, |DA| = √45, |AC| = √125, |BD| = √17; this gives a parallelogram (not a rectangle).

Q6. The points A(−3, 0), B(0, 4), C(3, 0) and D(0, −4) are the vertices of

• A. a rectangle (not a square)
• B. a square
• C. a parallelogram (not a rectangle)
• D. a rhombus (not a square)(correct answer)

Answer: D.Using the distance formula: |AB| = √25, |BC| = √25, |CD| = √25, |DA| = √25, |AC| = √36, |BD| = √64; this gives a rhombus (not a square).

Q7. The points A(0, 0), B(4, 3), C(8, 0) and D(4, −3) are the vertices of

• A. a square
• B. a parallelogram (not a rectangle)
• C. a rhombus (not a square)(correct answer)
• D. a rectangle (not a square)

Answer: C.Using the distance formula: |AB| = √25, |BC| = √25, |CD| = √25, |DA| = √25, |AC| = √64, |BD| = √36; this gives a rhombus (not a square).

Q8. The points A(−1, −1), B(2, −1), C(4, 2) and D(1, 2) are the vertices of

• A. a rhombus (not a square)
• B. a parallelogram (not a rectangle)(correct answer)
• C. a rectangle (not a square)
• D. a square

Answer: B.Using the distance formula: |AB| = √9, |BC| = √13, |CD| = √9, |DA| = √13, |AC| = √34, |BD| = √10; this gives a parallelogram (not a rectangle).

Q9. The points A(0, 0), B(7, 0), C(7, 3) and D(0, 3) are the vertices of

• A. a parallelogram (not a rectangle)
• B. a rectangle (not a square)(correct answer)
• C. a square
• D. a rhombus (not a square)

Answer: B.Using the distance formula: |AB| = √49, |BC| = √9, |CD| = √49, |DA| = √9, |AC| = √58, |BD| = √58; this gives a rectangle (not a square).

Q10. Exercise 9.3 Q3: the midpoints of the sides of a triangle are (2, 5), (4, 2), (1, 1). The three vertices are

• A. (5, 6), (1, 4), (3, 2)
• B. (3, 7), (1, 3), (5, 1)
• C. (7, 8), (−3, 2), (1, −4)
• D. (5, 6), (−1, 4), (3, −2)(correct answer)

Answer: D.Vertex = sum of two midpoints minus the third: (2 + 4 − 1, 5 + 2 − 1) = (5, 6); (2 + 1 − 4, 5 + 1 − 2) = (−1, 4); (4 + 1 − 2, 2 + 1 − 5) = (3, −2).