Coordinate Geometry for Competitive Exam Success

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Coordinate Geometry

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Coordinate Geometry MCQ & Objective Questions

Coordinate Geometry is a crucial topic for students preparing for school and competitive exams in India. Mastering this subject not only enhances your understanding of geometric concepts but also significantly boosts your exam scores. Practicing MCQs and objective questions helps in reinforcing your knowledge and identifying important questions that frequently appear in exams.

What You Will Practise Here

Understanding the Cartesian coordinate system and plotting points.
Key formulas for distance, midpoint, and section formula.
Equations of lines: slope-intercept form, point-slope form, and standard form.
Concepts of parallel and perpendicular lines in the coordinate plane.
Finding the area of triangles and other polygons using coordinates.
Applications of coordinate geometry in real-life problems.
Graphical representation of linear equations and inequalities.

Exam Relevance

Coordinate Geometry is a vital part of the mathematics syllabus for CBSE, State Boards, NEET, and JEE. Questions from this topic often include finding distances, determining slopes, and solving equations of lines. Students can expect to encounter both direct application questions and conceptual problems that test their understanding of the subject. Familiarity with common question patterns will aid in effective exam preparation.

Common Mistakes Students Make

Confusing the different forms of linear equations.
Miscalculating distances or midpoints due to sign errors.
Overlooking the significance of slopes in determining line relationships.
Failing to apply the correct formula in area calculations.

FAQs

Question: What is the importance of practicing Coordinate Geometry MCQ questions?
Answer: Practicing MCQ questions helps reinforce concepts, improves problem-solving speed, and boosts confidence for exams.

Question: How can I effectively prepare for Coordinate Geometry objective questions with answers?
Answer: Regular practice of important Coordinate Geometry questions for exams and reviewing mistakes can enhance your understanding and retention.

Start solving practice MCQs today to test your understanding and excel in your exams. Remember, consistent practice is the key to mastering Coordinate Geometry!

Distance Formula Ellipse Basics Equation of Circle Hyperbola Basics Parabola Basics Section Formula Straight Line

Q. Calculate the distance between the points (1, 1) and (4, 5).

A. 4
B. 5
C. 6
D. 7

Solution

Using the distance formula: d = √[(4 - 1)² + (5 - 1)²] = √[9 + 16] = √25 = 5.

Correct Answer: B — 5

Q. Calculate the distance between the points (1, 2) and (1, 5).

A. 3
B. 4
C. 2
D. 5

Solution

Using the distance formula: d = √[(1 - 1)² + (5 - 2)²] = √[0 + 9] = √9 = 3.

Correct Answer: A — 3

Q. Calculate the distance between the points (6, 8) and (2, 3).

A. 5
B. 6
C. 7
D. 8

Solution

Using the distance formula: d = √[(2 - 6)² + (3 - 8)²] = √[16 + 25] = √41.

Correct Answer: B — 6

Q. Calculate the distance between the points (6, 8) and (6, 2).

A. 6
B. 5
C. 4
D. 3

Solution

Using the distance formula: d = √((6 - 6)² + (2 - 8)²) = √(0 + 36) = √36 = 6.

Correct Answer: A — 6

Q. Determine the angle between the lines y = 2x + 1 and y = -1/2x + 3. (2021)

A. 90 degrees
B. 45 degrees
C. 60 degrees
D. 30 degrees

Solution

The slopes are m1 = 2 and m2 = -1/2. The angle θ = tan⁻¹(|(m1 - m2) / (1 + m1*m2)|) = tan⁻¹(5/3), which is approximately 90 degrees.

Correct Answer: A — 90 degrees

Q. Determine the distance between the points (-1, -1) and (2, 2).

A. 3
B. 4
C. 5
D. 6

Solution

Using the distance formula: d = √[(2 - (-1))² + (2 - (-1))²] = √[(2 + 1)² + (2 + 1)²] = √[9 + 9] = √18 = 3√2 ≈ 4.24.

Correct Answer: C — 5

Q. Determine the distance between the points (0, 0) and (0, 8).

A. 8
B. 6
C. 4
D. 2

Solution

Using the distance formula: d = √[(0 - 0)² + (8 - 0)²] = √[0 + 64] = √64 = 8.

Correct Answer: A — 8

Q. Determine the distance between the points (1, 2) and (4, 6). (2022)

A. 5
B. 4
C. 3
D. 6

Solution

Using the distance formula: d = √[(4 - 1)² + (6 - 2)²] = √[9 + 16] = √25 = 5.

Correct Answer: A — 5

Q. Determine the distance between the points (2, 3) and (2, -1).

A. 4
B. 5
C. 3
D. 2

Solution

Using the distance formula: d = √[(2 - 2)² + (-1 - 3)²] = √[0 + 16] = √16 = 4.

Correct Answer: A — 4

Q. Determine the distance from the point (1, 2) to the line 2x + 3y - 6 = 0. (2023)

A. 1
B. 2
C. 3
D. 4

Solution

Using the formula for distance from a point to a line, the distance is |2(1) + 3(2) - 6| / sqrt(2^2 + 3^2) = 1.

Correct Answer: B — 2

Q. Determine the x-intercept of the line given by the equation 5x + 2y - 10 = 0. (2023)

A. 2
B. 0
C. 5
D. 10

Solution

Setting y = 0 in the equation gives 5x = 10, thus x = 2. The x-intercept is 2.

Correct Answer: C — 5

Q. Determine the y-intercept of the line given by the equation 5x + 2y - 10 = 0. (2021)

A. 5
B. 2
C. 10
D. 0

Solution

Setting x = 0 in the equation gives 2y = 10, thus y = 5. The y-intercept is 5.

Correct Answer: B — 2

Q. Find the distance between the points (-1, -1) and (2, 2).

A. 3
B. 4
C. 5
D. 6

Solution

Using the distance formula: d = √[(2 - (-1))² + (2 - (-1))²] = √[9 + 9] = √18 = 3√2.

Correct Answer: C — 5

Q. Find the distance between the points (-2, -3) and (4, 5).

A. 8
B. 7
C. 6
D. 9

Solution

Using the distance formula: d = √[(4 - (-2))² + (5 - (-3))²] = √[(4 + 2)² + (5 + 3)²] = √[36 + 64] = √100 = 10.

Correct Answer: B — 7

Q. Find the distance between the points (0, 0) and (x, y) where x = 6 and y = 8.

A. 10
B. 8
C. 6
D. 12

Solution

Using the distance formula: d = √[(6 - 0)² + (8 - 0)²] = √[36 + 64] = √100 = 10.

Correct Answer: A — 10

Q. Find the distance between the points (1, 1) and (4, 5). (2023)

A. 5
B. 4
C. 3
D. 6

Solution

Using the distance formula: d = √[(4 - 1)² + (5 - 1)²] = √[9 + 16] = √25 = 5.

Correct Answer: A — 5

Q. Find the distance between the points (3, 3) and (3, 7).

A. 4
B. 5
C. 6
D. 7

Solution

Using the distance formula: d = √[(3 - 3)² + (7 - 3)²] = √[0 + 16] = √16 = 4.

Correct Answer: A — 4

Q. Find the distance between the points (3, 7) and (3, 1).

A. 6
B. 5
C. 4
D. 3

Solution

Using the distance formula: d = √((3 - 3)² + (1 - 7)²) = √(0 + 36) = √36 = 6.

Correct Answer: A — 6

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

A. 4
B. 5
C. 3
D. 2

Solution

Using the distance formula: d = √[(5 - 5)² + (1 - 5)²] = √[0 + 16] = √16 = 4.

Correct Answer: A — 4

Q. Find the equation of the line passing through the points (2, 3) and (4, 7). (2020)

A. y = 2x - 1
B. y = 2x + 1
C. y = 3x - 3
D. y = 2x + 3

Solution

The slope m = (7 - 3) / (4 - 2) = 2. Using point-slope form: y - 3 = 2(x - 2) gives y = 2x + 1.

Correct Answer: B — y = 2x + 1

Q. Find the point of intersection of the lines 2x + 3y = 6 and x - y = 1. (2020)

A. (0, 2)
B. (2, 0)
C. (1, 1)
D. (3, 0)

Solution

Solving the equations simultaneously, we find the intersection point is (1, 1).

Correct Answer: C — (1, 1)

Q. Find the point of intersection of the lines 2x + y = 10 and x - y = 1. (2020)

A. (3, 4)
B. (4, 2)
C. (2, 6)
D. (5, 0)

Solution

Solving the equations simultaneously, we find the intersection point is (3, 4).

Correct Answer: A — (3, 4)

Q. For the parabola defined by the equation x^2 = -12y, what is the direction in which it opens?

A. Upwards
B. Downwards
C. Left
D. Right

Solution

The equation x^2 = -12y indicates that the parabola opens downwards.

Correct Answer: C — Left

Q. For the parabola defined by the equation x^2 = 16y, what is the distance from the vertex to the focus?

A. 2
B. 4
C. 8
D. 16

Solution

In the equation x^2 = 4py, we have 4p = 16, thus p = 4. The distance from the vertex to the focus is 4.

Correct Answer: B — 4

Q. For the parabola defined by the equation x^2 = 16y, what is the length of the latus rectum?

A. 4
B. 8
C. 16
D. 2

Solution

The length of the latus rectum for the parabola x^2 = 4py is 4p. Here, p = 4, so the length is 8.

Correct Answer: B — 8

Q. For the parabola defined by the equation y = -x^2 + 4x - 3, what is the y-intercept?

A. -3
B. 0
C. 3
D. 4

Solution

To find the y-intercept, set x = 0. The equation becomes y = -0^2 + 4(0) - 3 = -3.

Correct Answer: A — -3

Q. If a line has an equation of the form y = mx + c, what does 'c' represent? (2023)

A. Slope
B. Y-intercept
C. X-intercept
D. None of the above

Solution

'c' represents the y-intercept of the line, which is the point where the line crosses the y-axis.

Correct Answer: B — Y-intercept

Q. If a line has the equation 4x - y + 8 = 0, what is its y-intercept? (2019)

A. 8
B. 4
C. -8
D. -4

Solution

Setting x = 0 in the equation gives y = 8. Thus, the y-intercept is -8.

Correct Answer: D — -4

Q. If a line has the equation 5x + 12y = 60, what is the x-intercept? (2019)

A. 12
B. 5
C. 60
D. 0

Solution

Setting y = 0 in the equation gives 5x = 60, thus x = 12.

Correct Answer: A — 12

Q. If a line has the equation 7x + 2y = 14, what is the slope of the line? (2023)

A. -7/2
B. 7/2
C. 2/7
D. -2/7

Solution

Rearranging to slope-intercept form gives y = -7/2x + 7, so the slope is -7/2.

Correct Answer: A — -7/2

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