Knowledge Check : Co-Ordinate Geometry
Knowledge Check
Cartesian Coordinate System
Q1: In which quadrant does the point (–4, –3) lie?
A) I
B) II
C) III
D) IV
Q2: What is the abscissa of the point (7, –2)?
A) 7
B) –2
C) 5
D) 9
Q3: Which point lies on the X-axis?
A) (5, 3)
B) (–6, 0)
C) (0, –7)
D) (4, –2)
Q4: Which of the following points lies on the Y-axis?
A) (0, 5)
B) (6, 0)
C) (–3, 2)
D) (4, –1)
Q5: If a point lies in the second quadrant, what are the signs of its coordinates?
A) (+, +)
B) (–, +)
C) (–, –)
D) (+, –)
Q6: The point (0,0) is called:
A) Origin
B) Abscissa
C) Ordinate
D) Intercept
Q7: Which quadrant contains the point (4, –9)?
A) I
B) II
C) III
D) IV
Q8: What is the ordinate of the point (–8, 6)?
A) –8
B) 6
C) 14
D) –6
Q9: A point with both coordinates positive lies in:
A) I quadrant
B) II quadrant
C) III quadrant
D) IV quadrant
Q10: Which point is the reflection of (3, 5) in the Y-axis?
A) (–3, 5)
B) (3, –5)
C) (–3, –5)
D) (5, 3)
Q11: A point (x, y) lies on the X-axis if:
A) x = 0
B) y = 0
C) x = y
D) x = –y
Q12: Which point is located exactly 5 units above origin?
A) (0, 5)
B) (5, 0)
C) (–5, 0)
D) (5, 5)
Q13: The coordinates of the origin are:
A) (1, 1)
B) (0, 1)
C) (1, 0)
D) (0, 0)
Q14: Which point lies exactly on the negative Y-axis?
A) (0, –4)
B) (–4, 0)
C) (–4, –4)
D) (4, –4)
Q15: How many quadrants are there in the Cartesian plane?
A) 2
B) 3
C) 4
D) 5
Q16: The sign of x and y both negative indicates:
A) First quadrant
B) Second quadrant
C) Third quadrant
D) Fourth quadrant
Q17: Which point is 6 units to the right of origin?
A) (6, 0)
B) (–6, 0)
C) (0, 6)
D) (0, –6)
Q18: Which axis divides the plane into upper and lower halves?
A) X-axis
B) Y-axis
C) Origin
D) Line y = x
Q19: The mirror image of point (–5, 2) across X-axis is:
A) (5, –2)
B) (–5, –2)
C) (5, 2)
D) (–2, 5)
Q20: Which point is 7 units below the origin?
A) (–7, 0)
B) (7, 0)
C) (0, 7)
D) (0, –7)
Distance Formula
Q21: Find the distance between points (2, 3) and (2, 8).
A) 3
B) 4
C) 5
D) 6
Q22: What is the distance between (−1, 4) and (3, 4)?
A) 2
B) 3
C) 4
D) 5
Q23: The distance between (0,0) and (6,8) is:
A) 8
B) 10
C) 12
D) 14
Q24: Find distance between (5, −2) and (5, 5).
A) 5
B) 6
C) 7
D) 8
Q25: Distance between (−3, −4) and (1, 2) is:
A) 6
B) 7
C) 8
D) 10
Q26: Distance between two identical points is always:
A) 1 unit
B) Zero
C) 2 units
D) Depends on position
Q27: Which formula represents distance between (x₁, y₁) and (x₂, y₂)?
A) √(x₁ + x₂ + y₁ + y₂)
B) √[(x₂ − x₁)² + (y₂ − y₁)²]
C) (x₂ + y₂)²
D) (x₁ − y₁)²
Q28: Find distance between (−2, 0) and (3, 0).
A) 3
B) 4
C) 5
D) 6
Q29: The distance from origin to point (9, 12) is:
A) 13
B) 15
C) 18
D) 20
Q30: If distance between two points is zero, what can we conclude?
A) They lie on X-axis
B) They lie on Y-axis
C) They coincide
D) They are symmetric
Q31: Find the distance between (2, −1) and (6, 2).
A) 3
B) 4
C) 5
D) 6
Q32: Which pair of points are 5 units apart?
A) (0,0) & (5,5)
B) (0,0) & (3,4)
C) (1,1) & (4,5)
D) (2,2) & (6,7)
Q33: Distance between (−5, 2) and (−5, −3) is:
A) 3
B) 4
C) 5
D) 6
Q34: The distance between two points on the X-axis depends only on:
A) Y-coordinates
B) X-coordinates
C) Both X and Y
D) Origin only
Q35: Distance between (7, 1) and (1, 1) is:
A) 4
B) 5
C) 6
D) 7
Q36: If A(1,2) and B(4,6) are given, distance AB is:
A) 3
B) 4
C) 5
D) 6
Q37: Distance from origin to (0, −9) is:
A) 7
B) 8
C) 9
D) 10
Q38: What is the distance between (–4, –3) and (–4, 3)?
A) 4
B) 5
C) 6
D) 7
Q39: If distance between two points is √25, the distance is:
A) 3
B) 4
C) 5
D) 6
Q40: Two points differ only in y-coordinate, then the distance equals:
A) Difference of x-values
B) Difference of y-values
C) Product of x-values
D) Sum of coordinates
Section Formula
Q41: Find coordinates of midpoint of (2, 4) and (6, 8).
A) (3, 6)
B) (4, 6)
C) (5, 7)
D) (2, 8)
Q42: Which formula gives coordinates of midpoint?
A) ((x₁−x₂)/2, (y₁−y₂)/2)
B) ((x₁+x₂)/2, (y₁+y₂)/2)
C) (2x₁, 2y₁)
D) (x₂−x₁, y₂−y₁)
Q43: Midpoint of (−4, 2) and (4, 2) is:
A) (2, 2)
B) (0, 0)
C) (0, 2)
D) (−2, 2)
Q44: A point divides a line internally in ratio 1:1. It is:
A) Origin
B) Midpoint
C) Endpoint
D) Centroid
Q45: Find the midpoint of (5, 0) and (5, 10).
A) (5, 4)
B) (5, 5)
C) (0, 5)
D) (10, 5)
Q46: A point P divides AB internally in ratio 2:1. What does this mean?
A) P is outside AB
B) AP = 2 × PB
C) PB = 2 × AP
D) AP = PB
Q47: If midpoint of A and B is (3,4) and A is (1,2), coordinates of B are:
A) (4,6)
B) (5,6)
C) (6,8)
D) (7,8)
Q48: Which formula finds the point dividing a line internally in ratio m:n?
A) ((mx₁+nx₂)/(m+n), (my₁+ny₂)/(m+n))
B) ((x₁+x₂)/2)
C) ((x₁−x₂)/(m+n))
D) (x₁+x₂)
Q49: A point divides segment joining (0,0) and (8,0) in ratio 1:3. Its x-coordinate is:
A) 1
B) 2
C) 3
D) 6
Q50: The midpoint of diagonal of a square lies at:
A) At origin always
B) At centre of square
C) On one vertex
D) Outside square
Q51: If endpoints are (2,2) and (8,6), midpoint is:
A) (4,4)
B) (5,4)
C) (6,4)
D) (4,6)
Q52: A point dividing a line segment externally lies:
A) Between endpoints
B) On the line but outside segment
C) Only at midpoint
D) Always on origin
Q53: Midpoint of points with same x-coordinate lies on:
A) X-axis
B) Y-axis
C) Vertical line
D) Horizontal line
Q54: Which of the following divides a triangle into three equal area parts?
A) Perpendicular bisector
B) Median
C) Altitude
D) Diagonal
Q55: The centroid divides each median in the ratio:
A) 1:1
B) 1:2
C) 2:1
D) 3:1
Q56: The centroid of triangle with vertices (0,0), (6,0), (0,6) is:
A) (2,2)
B) (3,3)
C) (4,4)
D) (5,5)
Q57: The midpoint of a segment divides it into two segments which are:
A) Unequal
B) Equal
C) Perpendicular
D) Parallel
Q58: A line joining midpoint of two sides of triangle is parallel to:
A) First side
B) Second side
C) Third side
D) Base always
Q59: Section formula is used to find:
A) Length of line
B) Slope of line
C) Coordinates of a point dividing line
D) Area of triangle
Q60: A point divides the line joining (1,3) and (5,7) in ratio 1:1. The point is:
A) (2,4)
B) (3,5)
C) (4,6)
D) (5,5)
Knowledge Check
Straight Lines
Q61: The slope of a horizontal line is:
A) 0
B) 1
C) Undefined
D) Infinite
Q62: The slope of a vertical line is:
A) 0
B) 1
C) Undefined
D) -1
Q63: The slope of line joining (2,3) and (6,7) is:
A) 1/2
B) 1
C) 2
D) 4
Q64: Two lines are parallel if their slopes are:
A) Equal
B) Negative reciprocal
C) Zero
D) Undefined
Q65: Two lines are perpendicular if product of their slopes is:
A) 0
B) 1
C) −1
D) 2
Q66: The slope of line x + 2y = 4 is:
A) −1/2
B) 2
C) −2
D) 1/2
Q67: A line with slope 0 is parallel to:
A) X-axis
B) Y-axis
C) origin
D) diagonal
Q68: A line parallel to y-axis has equation:
A) y = 0
B) x = a
C) y = mx + c
D) x + y = 0
Q69: If slope of a line is negative, the line is:
A) Increasing left to right
B) Vertical
C) Decreasing left to right
D) Horizontal
Q70: A line passing through origin with slope 2 has equation:
A) y = x + 2
B) y = 2x
C) 2y = x
D) x = 2y
Q71: The slope of line joining (−2,4) and (2,0) is:
A) 1
B) −1
C) −2
D) 2
Q72: If slope is positive, the line rises towards:
A) Left side
B) Right side
C) Downwards
D) Both sides
Q73: A line perpendicular to y = 2x has slope:
A) 2
B) 1/2
C) −1/2
D) −2
Q74: A line making angle 45° with X-axis has slope:
A) 0
B) 1
C) 2
D) −1
Q75: A line passing through (0,3) and parallel to X-axis has equation:
A) x = 3
B) y = 3
C) y = x + 3
D) x + y = 3
Q76: If slope of two lines are m and m₂, perpendicular condition is:
A) m + m₂ = 0
B) m = m₂
C) mm₂ = −1
D) mm₂ = 1
Q77: Slope of line joining (1,1) and (3,5) is:
A) 1
B) 2
C) 3
D) 4
Q78: A line is parallel to Y-axis if its equation has form:
A) y = constant
B) x = constant
C) y = mx + c
D) ax + by = c
Q79: If a line makes 90° with X-axis, it is:
A) Horizontal
B) Vertical
C) Normal
D) Diagonal
Q80: Which of the following represents slope?
A) Δx/Δy
B) Δy/Δx
C) x/y
D) y/x
Knowledge Check
Straight Lines
Q81: The slope of a line joining (4,2) and (4,6) is:
A) 0
B) 1
C) Undefined
D) −1
Q82: The slope of a line passing through (0,0) and (5,0) is:
A) 5
B) 0
C) −5
D) Undefined
Q83: If slope of a line is 3, the line:
A) Is horizontal
B) Is vertical
C) Rises steeply left to right
D) Falls left to right
Q84: Which line is perpendicular to y = −2x + 5?
A) y = 2x − 5
B) y = (1/2)x + 3
C) y = −(1/2)x + 2
D) y = −2x + 1
Q85: A line passing through (2,3) with slope 1 has equation:
A) y = x + 1
B) y = x + 5
C) y = x − 1
D) y = 2x + 3
Q86: A line making an angle of 135° with X-axis has slope:
A) 1
B) −1
C) 0
D) √3
Q87: A line parallel to y = −3x + 7 has slope:
A) 3
B) −3
C) 1/3
D) −1/3
Q88: What is the slope of the line x − y + 2 = 0?
A) 1
B) −1
C) 2
D) −2
Q89: A line with equation y = 4 is:
A) Vertical line
B) Horizontal line
C) Inclined line
D) Diagonal line
Q90: Two lines are perpendicular if slopes are 2 and:
A) −2
B) 1/2
C) −1/2
D) 2
Q91: The slope of a line is positive if:
A) It rises right to left
B) It falls left to right
C) It rises left to right
D) It is vertical
Q92: A line passes through (1,2) and is parallel to X-axis. Its equation is:
A) x = 2
B) x = 1
C) y = 2
D) y = 1
Q93: The line y = −3x + 4 makes what angle with X-axis?
A) Acute
B) Obtuse
C) Right angle
D) Straight angle
Q94: A line through the origin making 30° with X-axis has slope:
A) √3
B) 1/√3
C) 2
D) 0
Q95: Which equation represents a vertical line?
A) y = 5
B) x = −2
C) y = 2x
D) y + x = 3
Q96: A line perpendicular to X-axis will be:
A) Horizontal
B) Vertical
C) Parallel to X-axis
D) Slanted
Q97: A line through (3,0) perpendicular to X-axis is:
A) y = 3
B) x = 3
C) y = 0
D) x = 0
Q98: A line making 0° with the X-axis is:
A) Horizontal
B) Vertical
C) Diagonal
D) Normal
Q99: The equation y = mx + c represents:
A) Circle
B) Straight line
C) Parabola
D) Hyperbola
Q100: If slope of two parallel lines is 4, then slope of each is:
A) 1/4
B) −4
C) 4
D) −1/4