Knowledge Check : Co-Ordinate Geometry
Knowledge Check
Introduction to Coordinate Geometry
Q1: The point (0, 0) in the Cartesian plane is called
A) Abscissa
B) Ordinate
C) Origin
D) Coordinate
Q2: In which quadrant does the point (–5, 3) lie?
A) First
B) Second
C) Third
D) Fourth
Q3: The abscissa of any point on the y-axis is
A) 0
B) 1
C) –1
D) Any number
Q4: Point (4, –7) lies in which quadrant?
A) First
B) Second
C) Third
D) Fourth
Q5: The coordinates of a point on the x-axis are of the form
A) (x, 0)
B) (0, y)
C) (x, y)
D) (0, 0)
Q6: Which of the following points lies in the third quadrant?
A) (–3, 5)
B) (4, –2)
C) (–2, –6)
D) (7, 3)
Q7: The ordinate of the point (–8, 0) is
A) –8
B) 0
C) 8
D) Cannot be determined
Q8: Distance of point (0, 5) from origin is
A) 0
B) 5 units
C) 25 units
D) 10 units
Q9: In the Cartesian plane, the horizontal line is called
A) Y-axis
B) X-axis
C) Ordinate
D) Abscissa
Q10: Point (–3, 4) and (3, 4) lie on the same
A) Vertical line
B) Horizontal line
C) Slanting line
D) Origin
Q11: The point (6, –6) lies on the line
A) y = x
B) y = –x
C) x = 6
D) y = 6
Q12: Which point does NOT lie on the x-axis?
A) (5, 0)
B) (–7, 0)
C) (0, 0)
D) (3, –2)
Q13: The coordinates of Jaipur are approximately (75°E, 27°N). Its location is in
A) First quadrant
B) Second quadrant
C) Third quadrant
D) Fourth quadrant
Q14: Point (0, –9) lies on
A) Positive x-axis
B) Negative y-axis
C) Positive y-axis
D) Negative x-axis
Q15: The perpendicular distance of point (4, 7) from x-axis is
A) 4 units
B) 7 units
C) 11 units
D) 3 units
Q16: Which of the following points lies in the second quadrant?
A) (–5, –3)
B) (–4, 6)
C) (8, –2)
D) (7, 9)
Q17: The point of intersection of the two axes is
A) (1, 1)
B) (0, 1)
C) (1, 0)
D) (0, 0)
Q18: Distance of the point (–6, 8) from origin is
A) 10 units
B) 14 units
C) 2 units
D) 48 units
Q19: The point (5, 0) lies on
A) Positive y-axis
B) Negative x-axis
C) Positive x-axis
D) Negative y-axis
Q20: In a school playground, if the flag post is taken as origin, the canteen is at (0, 15) m. It lies on
A) Positive x-axis
B) Negative y-axis
C) Positive y-axis
D) Negative x-axis
Category 2: Distance Formula & Section Formula (Q21–Q40)
Q21: What is the distance between the points (2, 3) and (6, 3)?
A) 2 units
B) 3 units
C) 4 units
D) 6 units
Q22: Using the distance formula, what is the distance between (1, 2) and (4, 6)?
A) 4
B) 5
C) √13
D) √25
Q23: Find the distance between the points (−2, 1) and (2, 1).
A) 2 units
B) 4 units
C) 6 units
D) 8 units
Q24: What is the distance between (0, 0) and (3, 4)?
A) 5
B) 6
C) 7
D) 4
Q25: If the coordinates of a point are (x, y), what is the distance from the origin?
A) x + y
B) √(x − y)
C) √(x² + y²)
D) (x² + y²)
Q26: What are the coordinates of the midpoint of (2, 4) and (6, 8)?
A) (3, 5)
B) (4, 6)
C) (5, 7)
D) (6, 10)
Q27: A point divides the segment joining (2, 2) and (8, 2) in the ratio 1:1. What is the point?
A) (3, 2)
B) (4, 2)
C) (5, 2)
D) (6, 2)
Q28: Find the coordinates of the point dividing (0, 0) and (6, 0) internally in the ratio 1:2.
A) (2, 0)
B) (3, 0)
C) (4, 0)
D) (1, 0)
Q29: The midpoint of a segment is (4, 5). If one end is (2, 3), what is the other end?
A) (6, 7)
B) (5, 6)
C) (6, 5)
D) (7, 8)
Q30: Two points are (1, 1) and (5, 4). What is their distance?
A) √13
B) 5
C) √25
D) 6
Q31: A point divides the line joining (−4, 0) and (4, 0) in the ratio 3:1. What is its x-coordinate?
A) 1
B) 2
C) 0
D) −1
Q32: The length of a line segment joining (0, b) and (a, 0) is:
A) a + b
B) √(a² + b²)
C) (a² + b²)
D) a − b
Q33: If a point divides the line joining (2, 2) and (8, 6) in the ratio 2:1, what is the point?
A) (4, 3)
B) (6, 4)
C) (5, 4)
D) (3, 3)
Q34: The coordinates of the midpoint of (x1, y1) and (x2, y2) is:
A) (x1+x2, y1+y2)
B) ((x2−x1)/2, (y2−y1)/2)
C) ((x1+x2)/2, (y1+y2)/2)
D) (x1x2, y1y2)
Q35: If the distance between two points is zero, the points are:
A) Collinear
B) Identical
C) Perpendicular
D) Parallel
Q36: What is the distance between points (−3, 4) and (−3, 10)?
A) 6
B) 7
C) 13
D) 14
Q37: A point lies 5 units away from the origin on the x-axis. What can its coordinates be?
A) (5, 0) only
B) (−5, 0) only
C) (0, 5) only
D) (5, 0) and (−5, 0)
Q38: A point P divides QR in the ratio 1:3. This means P is:
A) Closer to R
B) Closer to Q
C) Midpoint
D) Outside QR
Q39: The point (a, 0) lies on:
A) y-axis
B) x-axis
C) Origin only
D) y = x line
Q40: Find the ratio in which the point (2, 2) divides the line joining (0, 0) and (6, 6).
A) 1:1
B) 1:2
C) 2:1
D) 3:1
Straight Lines and Slope
Q41: The slope of a line parallel to the x-axis is
A) 0
B) 1
C) Undefined
D) –1
Q42: The slope of the line x = 5 is
A) 0
B) 1
C) Undefined
D) 5
Q43: Slope of the line joining (2, 3) and (7, 3) is
A) 0
B) 5
C) 1
D) Undefined
Q44: Slope of the line joining (–1, 4) and (–1, –2) is
A) 0
B) 6
C) –6
D) Undefined
Q45: Slope of line joining (0, 0) and (5, 10) is
A) 1/2
B) 2
C) 5
D) 10
Q46: The slope of the line y = –3x + 4 is
A) –3
B) 3
C) 4
D) –4
Q47: Two lines are perpendicular if the product of their slopes is
A) 0
B) 1
C) –1
D) Undefined
Q48: Slope of line joining Chennai (13°N) and Delhi (28°N) on a simplified map is
A) Positive
B) Negative
C) Zero
D) Undefined
Q49: If slope of a line is 1/2, slope of line perpendicular to it is
A) 2
B) –2
C) 1/2
D) –1/2
Q50: The line joining (3, 5) and (8, –2) has slope
A) 7/5
B) –7/5
C) 5/7
D) –5/7
Q51: The slope of National Highway NH-44 from Srinagar to Kanyakumari is approximately
A) Positive
B) Negative
C) Zero
D) Undefined
Q52: If two lines have slopes 3 and –1/3, then they are
A) Parallel
B) Perpendicular
C) Coincident
D) Intersecting but not perpendicular
Q53: Slope of the line passing through (0, 7) and (4, 7) is
A) 0
B) 4
C) 7
D) Undefined
Q54: The slope of a line making 45° with positive x-axis is
A) 0
B) 1
C) –1
D) Undefined
Q55: If slope of a road is –1/5, it means for every 5 m horizontal the road drops
A) 1 m
B) 5 m
C) 1/5 m
D) 25 m
Q56: The line joining points (2, –3) and (–4, 5) has slope
A) 4/3
B) –4/3
C) 3/4
D) –3/4
Q57: Slope of the line y = 7 is
A) 0
B) 7
C) Undefined
D) 1
Q58: Two lines with slopes 2 and 2 are
A) Perpendicular
B) Parallel
C) Intersecting
D) Coincident
Q59: The slope of a staircase making 135° with positive x-axis is
A) 1
B) –1
C) 0
D) Undefined
Q60: If three points have the same slope between each pair, the points are
A) Collinear
B) Form a triangle
C) Form a rectangle
D) Form a parallelogram
Area and Collinearity + Mixed Revision
Q61: The area of triangle with vertices (0,0), (6,0) and (0,8) is
A) 24 sq units
B) 48 sq units
C) 12 sq units
D) 30 sq units
Q62: Points (1,2), (3,2) and (5,2) are
A) Collinear
B) Form a triangle of area 6
C) Form a triangle of area 0
D) Non-collinear
Q63: Area of triangle with vertices (2,3), (2,7) and (5,7) is
A) 6 sq units
B) 0 sq units
C) 12 sq units
D) 15 sq units
Q64: If area of triangle formed by (1,1), (k,2) and (4,5) is zero, then k =
A) 2
B) 3
C) 4
D) 1
Q65: Using Heron’s formula is used in coordinate geometry when we first find
A) Area directly
B) Three sides using distance formula, then apply Heron’s
C) Centroid
D) Slope
Q66: Area of triangle with vertices (–1,–1), (2,3), (5,–1) is
A) 10 sq units
B) 12 sq units
C) 8 sq units
D) 0
Q67: Points A(3,4), B(6,4), C(9,8) are collinear because
A) Area is zero
B) Slope AB = Slope BC
C) Both A and B
D) Distance AB = BC
Q68: Three vertices of a parallelogram are (0,0), (4,0), (6,3). The fourth vertex is
A) (2,3)
B) (10,3)
C) (1,3)
D) (2,–3)
Q69: In a school campus map, library (0,0), canteen (5,0), playground (0,7). Area of triangular field is
A) 35/2 sq units
B) 35 sq units
C) 17.5 sq units
D) Both A and C
Q70: Points (1,1), (2,3), (3,5) are collinear because slope is constant
A) 2
B) 1
C) 3
D) 0
Q71: Area of triangle formed by points (4,1), (7,1), (4,6) is
A) 15/2 sq units
B) 15 sq units
C) 7.5 sq units
D) 0
Q72: If points A(2,3), B(5,k), C(8,3) are collinear, then k =
A) 3
B) 4
C) 5
D) 6
Q73: The points (0,0), (a,0), (0,b) always form
A) Right-angled triangle
B) Isosceles triangle
C) Equilateral triangle
D) Scalene triangle
Q74: Using Heron’s formula, area of triangle with sides 5, 5, 6 units is
A) 12 sq units
B) 15 sq units
C) 10 sq units
D) 20 sq units
Q75: Three consecutive vertices of a rectangle are (0,0), (8,0), (8,5). Fourth vertex is
A) (0,5)
B) (5,8)
C) (0,8)
D) (8,5)
Q76: The point dividing the line joining (–2,4) and (6,10) in ratio 1:3 is
A) (1,6)
B) (2,7)
C) (0,6)
D) (4,8)
Q77: Area of triangle formed by points (1,–1), (5,2), (9,–1) is
A) 10 sq units
B) 12 sq units
C) 8 sq units
D) 14 sq units
Q78: The centroid of triangle with vertices (1,2), (4,6), (7,10) is
A) (4, 6)
B) (12,18)
C) (6, 9)
D) (3, 6)
Q79: In a village map, well (0,0), temple (10,0), school (5,5√3). The triangle is
A) Equilateral
B) Isosceles
C) Right-angled
D) Scalene
Q80: If four points form a rectangle, the diagonals are equal and their mid-points
A) Are different
B) Coincide
C) Are perpendicular
D) Are parallel