Distance formula MCQs With Answer

Distance formula MCQs With Answer for B. Pharm students provides a focused review of coordinate geometry concepts used in pharmaceutical calculations, microscopy measurements, molecular spacing, and formulation geometry. This concise, Student-friendly post covers 2D and 3D distance formulas, point-to-line and point-to-plane distances, midpoint and section formula connections, and practical unit conversions commonly encountered in lab work. Ideal for exam prep and competitive tests, these MCQs reinforce problem-solving skills and real-world pharmacy applications like particle size assessment and imaging measurements. Keywords: Distance formula MCQs With Answer, distance formula, B. Pharm, coordinate geometry, pharmacy students.
Now let’s test your knowledge with 50 MCQs on this topic.

Q1. What is the distance between the points (0, 0) and (3, 4)?

• 4
• 5
• 6
• 7

Correct Answer: 5

Q2. Using the distance formula, the distance between (1, 2) and (4, 6) is:

• 3
• 4
• 5
• 6

Correct Answer: 5

Q3. The distance between (-1, -1) and (2, 3) equals:

• 4
• 5
• 6
• √10

Correct Answer: 5

Q4. What is the standard 2D distance formula between points (x1, y1) and (x2, y2)?

• √[(x1+x2)^2 + (y1+y2)^2]
• √[(x2−x1)^2 + (y2−y1)^2]
• |x2−x1| + |y2−y1|
• [(x2−x1) + (y2−y1)]^2

Correct Answer: √[(x2−x1)^2 + (y2−y1)^2]

Q5. Distance between (2, −1) and (−2, 3) is:

• 4
• 4√2
• 8
• 6

Correct Answer: 4√2

Q6. Which expression gives the squared distance between two 2D points (x1, y1) and (x2, y2)?

• (x2 + x1)^2 + (y2 + y1)^2
• (x2 − x1)^2 + (y2 − y1)^2
• √[(x2 − x1)^2 + (y2 − y1)^2]
• |x2 − x1|·|y2 − y1|

Correct Answer: (x2 − x1)^2 + (y2 − y1)^2

Q7. In 3D, the distance between (1, 2, 3) and (4, 6, 3) is:

• 3
• 4
• 5
• √50

Correct Answer: 5

Q8. Distance from origin to point (1, 1, 1) in 3D is:

• 1
• √2
• √3
• 3

Correct Answer: √3

Q9. The distance between (2, 3, 5) and (2, 3, 9) equals:

• 2
• 3
• 4
• √20

Correct Answer: 4

Q10. If every coordinate of two points is multiplied by 2, how does the distance between them change?

• It remains the same
• It doubles
• It halves
• It quadruples

Correct Answer: It doubles

Q11. The midpoint formula for two points (x1, y1) and (x2, y2) is:

• ((x1−x2)/2, (y1−y2)/2)
• ((x1+x2)/2, (y1+y2)/2)
• ((x2/x1), (y2/y1))
• ((x1+x2), (y1+y2))

Correct Answer: ((x1+x2)/2, (y1+y2)/2)

Q12. If midpoint of A(2, 1) and B is (3, 4), what are B’s coordinates?

• (1, 3)
• (4, 7)
• (5, 6)
• (2, 4)

Correct Answer: (4, 7)

Q13. The section formula for internal division in ratio m:n for points (x1,y1) and (x2,y2) gives the x-coordinate as:

• (mx2 + nx1)/(m + n)
• (mx1 + nx2)/(m + n)
• (x1 + x2)/(m + n)
• (m + n)/(mx1 + nx2)

Correct Answer: (mx1 + nx2)/(m + n)

Q14. The perpendicular distance from point (x0, y0) to line Ax + By + C = 0 is given by:

• |Ax0 + By0 + C|
• |Ax0 + By0 + C|/(A + B + C)
• |Ax0 + By0 + C|/√(A^2 + B^2)
• (Ax0 + By0 + C)^2/(A^2 + B^2)

Correct Answer: |Ax0 + By0 + C|/√(A^2 + B^2)

Q15. Distance from point (1, 2) to line 3x + 4y − 10 = 0 is:

• 0.2
• 1
• 2
• 0

Correct Answer: 0.2

Q16. Distance between parallel lines ax + by + c1 = 0 and ax + by + c2 = 0 is:

• |c1 + c2|/√(a^2 + b^2)
• |c2 − c1|/√(a^2 + b^2)
• |c2 − c1|/(a + b)
• √(c2 − c1)

Correct Answer: |c2 − c1|/√(a^2 + b^2)

Q17. The perpendicular distance from point (x0, y0, z0) to plane Ax + By + Cz + D = 0 is:

• |Ax0 + By0 + Cz0 + D|/(A + B + C)
• |Ax0 + By0 + Cz0 + D|/√(A^2 + B^2 + C^2)
• |Ax0 + By0 + Cz0 + D|
• √(Ax0 + By0 + Cz0 + D)

Correct Answer: |Ax0 + By0 + Cz0 + D|/√(A^2 + B^2 + C^2)

Q18. Distance from point (1, 0, 0) to plane x + y + z − 1 = 0 is:

• 1/√3
• 0
• 1
• √3

Correct Answer: 0

Q19. For a circle with center (0, 0), the radius to point (3, 4) is:

• 7
• 5
• √7
• 1

Correct Answer: 5

Q20. Convert 0.5 nanometers (nm) to angstroms (Å):

• 0.05 Å
• 0.5 Å
• 5 Å
• 50 Å

Correct Answer: 5 Å

Q21. If two points are endpoints of a diameter of a circle, the center is:

• Midpoint of the two endpoints
• One of the endpoints
• At origin always
• Equidistant from y-axis only

Correct Answer: Midpoint of the two endpoints

Q22. In pharmacy imaging, if two marked points at (10, 20) and (13, 24) are in pixels, the pixel distance is:

• 3
• 4
• 5
• √25

Correct Answer: 5

Q23. Distance between centers of two spheres at (0, 0, 0) and (2, 3, 6) is:

• 7
• √49
• √(4 + 9 + 36)
• √13

Correct Answer: √(4 + 9 + 36)

Q24. The shortest distance between two skew lines in 3D involves which vector operation?

• Dot product only
• Cross product and dot product
• Only scalar multiplication
• Matrix inversion

Correct Answer: Cross product and dot product

Q25. The triangle inequality for distances states which of the following?

• AB ≥ AC + CB
• AB = AC + CB
• AB ≤ AC + CB
• AB × AC = CB

Correct Answer: AB ≤ AC + CB

Q26. Which metric measures distance as |x2−x1| + |y2−y1| and is useful in grid-based models?

• Euclidean distance
• Hamming distance
• Manhattan (L1) distance
• Chebyshev distance

Correct Answer: Manhattan (L1) distance

Q27. In QSAR studies, Euclidean distance between descriptor vectors is used to:

• Measure molecular similarity
• Calculate melting point directly
• Predict pH of solution
• Determine solubility constant analytically

Correct Answer: Measure molecular similarity

Q28. Two particles have centers at (0,0,0) and (2,0,0) with radii 0.6 nm each. Do they overlap?

• Yes, they overlap
• No, they do not overlap
• They just touch
• Impossible to determine

Correct Answer: No, they do not overlap

Q29. Pixel coordinates change from (100, 200) to (150, 240). Distance in pixels is:

• 50
• 40
• √(50^2 + 40^2)
• 90

Correct Answer: √(50^2 + 40^2)

Q30. Points P(1,2), Q(4,2), R(4,6) form which type of triangle?

• Equilateral
• Isosceles
• Right-angled
• Obtuse

Correct Answer: Right-angled

Q31. The distance formula is derived directly from which fundamental theorem?

• Binomial theorem
• Pythagorean theorem
• Fermat’s little theorem
• Central limit theorem

Correct Answer: Pythagorean theorem

Q32. When optimizing to find the closest point, why is squared distance often used?

• Squared distance is always smaller
• To avoid square roots and simplify calculus
• Squared distance gives different minimizer
• It’s required by geometry rules

Correct Answer: To avoid square roots and simplify calculus

Q33. Generalization of the Euclidean distance to n-dimensions uses which formula?

• Sum of absolute differences
• Square root of sum of squared coordinate differences
• Product of coordinate differences
• Average of coordinate values

Correct Answer: Square root of sum of squared coordinate differences

Q34. The distance between (x, y) and (x + a, y + b) simplifies to:

• √(a^2 + b^2)
• √(x^2 + y^2)
• √((x+a)^2 + (y+b)^2)
• a + b

Correct Answer: √(a^2 + b^2)

Q35. If two points have identical coordinates, their distance is:

• 1
• 0
• Undefined
• Infinity

Correct Answer: 0

Q36. Distance from origin to point (−3, 4) equals:

• 1
• 5
• 7
• √13

Correct Answer: 5

Q37. Distance between (1/2, 1/2) and (−1/2, −1/2) is:

• 1
• √2
• 2
• 1/2

Correct Answer: √2

Q38. In biomedical imaging, measuring tumor diameter from pixel coordinates relies on:

• Distance formula after calibration from pixels to physical units
• Counting pixels only without calibration
• Using only Manhattan distance
• Assuming circular shape always

Correct Answer: Distance formula after calibration from pixels to physical units

Q39. The shortest distance from a point to a line segment may be:

• Projection point if it lies within segment, otherwise nearest endpoint
• Always the perpendicular projection regardless
• Always an endpoint
• Equal to half the segment length

Correct Answer: Projection point if it lies within segment, otherwise nearest endpoint

Q40. Distance between (0, 0, 5) and (0, 12, 0) is:

• 13
• 12
• 5
• √169

Correct Answer: 13

Q41. Distance between centers (1, 2, 3) and (4, 6, 7) equals:

• √(3^2 + 4^2 + 4^2)
• 10
• √41
• Both first and third are equivalent

Correct Answer: Both first and third are equivalent

Q42. If the distance between two points is zero, then:

• The points are identical
• They are opposite
• They are perpendicular
• They lie on a circle

Correct Answer: The points are identical

Q43. Is the Euclidean distance invariant under translation of the coordinate system?

• Yes, distances remain the same
• No, distances change
• Only if rotated too
• Only in 2D

Correct Answer: Yes, distances remain the same

Q44. Under dilation by factor k about the origin, distances scale by:

• k^2
• k
• 1/k
• √k

Correct Answer: k

Q45. The squared Euclidean distance between (x1, y1) and (x2, y2) equals:

• (x1 + x2)^2 + (y1 + y2)^2
• (x2 − x1)^2 + (y2 − y1)^2
• √[(x2 − x1)^2 + (y2 − y1)^2]
• |x2 − x1| + |y2 − y1|

Correct Answer: (x2 − x1)^2 + (y2 − y1)^2

Q46. Distance between (1, 1, 1) and (2, 3, 6) is approximately:

• √30
• 5.477
• Both first and second (equivalent)
• 6

Correct Answer: Both first and second (equivalent)

Q47. For practical lab measurements, why is it important to convert coordinates to consistent physical units before applying the distance formula?

• To ensure numerical stability only
• To obtain physically meaningful distances and avoid unit mismatch
• To reduce computation time
• It is not necessary

Correct Answer: To obtain physically meaningful distances and avoid unit mismatch

Q48. Which metric always satisfies non-negativity, identity, symmetry, and triangle inequality?

• Euclidean metric
• Non-metric similarity
• Arbitrary dissimilarity
• Only Manhattan metric

Correct Answer: Euclidean metric

Q49. Which formula is used to compute great-circle distance on Earth’s surface (relevant when mapping sample locations globally)?

• Euclidean distance formula in 3D Cartesian only
• Haversine formula
• Pythagorean theorem in latitude-longitude directly
• Manhattan distance on spherical grid

Correct Answer: Haversine formula

Q50. If coordinates are recorded in centimeters and you convert them to millimeters before computing distance, how does the computed distance change?

• It decreases by factor 10
• It increases by factor 10
• It remains unchanged
• It becomes 100 times larger

Correct Answer: It increases by factor 10

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