MTH101 Coordinates, Graphs, Lines - 100 MCQs with Answers | VU Mathematics (MTH101)
MTH101 Coordinates, Graphs, Lines - 100 MCQs with Answers | VU Mathematics
- What are the coordinates of the origin in a Cartesian plane?
- a) (0, 0)
- b) (1, 0)
- c) (0, 1)
- d) (1, 1)
Answer: a) (0, 0)
- Which quadrant contains points where both x and y are positive?
- a) Quadrant I
- b) Quadrant II
- c) Quadrant III
- d) Quadrant IV
Answer: a) Quadrant I
- What is the distance between points (3, 4) and (7, 1)?
Answer: c) √29
- The slope of a horizontal line is:
- a) 0
- b) 1
- c) Undefined
- d) Infinity
Answer: a) 0
- What is the midpoint of the line segment joining (2, 3) and (4, 7)?
- a) (3, 5)
- b) (6, 10)
- c) (1, 2)
- d) (2, 7)
Answer: a) (3, 5)
- Which formula is used to find the slope between two points (x1, y1) and (x2, y2)?
- a) (y2 - y1) / (x2 - x1)
- b) (x2 - x1) / (y2 - y1)
- c) (x1 + x2) / 2
- d) (y1 + y2) / 2
Answer: a) (y2 - y1) / (x2 - x1)
- Which of these is the equation of a vertical line?
- a) y = 5
- b) x = 5
- c) y = x + 5
- d) y = -x + 5
Answer: b) x = 5
- What is the slope of the line y = 3x + 2?
Answer: b) 3
- The line passes through points (1, 2) and (3, 6). What is its slope?
Answer: a) 2
- Which coordinate pair lies on the line y = 2x + 1?
- a) (1, 3)
- b) (2, 5)
- c) (0, 1)
- d) All of the above
Answer: d) All of the above
- The distance between (0, 0) and (0, 7) is:
- a) 7
- b) 0
- c) 49
- d) Undefined
Answer: a) 7
- What is the x-intercept of the line y = 3x - 6?
Answer: a) 2
- What is the y-intercept of the line 4x + 2y = 8?
Answer: a) 2
- Which is the correct formula for distance between two points?
- a) √((x2 - x1)^2 + (y2 - y1)^2)
- b) (x2 - x1) + (y2 - y1)
- c) (x2 + x1) / 2
- d) (y2 + y1) / 2
Answer: a) √((x2 - x1)^2 + (y2 - y1)^2)
- What is the slope of the line passing through (0, 0) and (5, 5)?
- a) 1
- b) 0
- c) 5
- d) Undefined
Answer: a) 1
- Which line has an undefined slope?
- a) y = 3x + 1
- b) x = 4
- c) y = -2x + 3
- d) y = 0
Answer: b) x = 4
- The midpoint of the points (-2, 3) and (4, 7) is:
- a) (1, 5)
- b) (2, 4)
- c) (3, 6)
- d) (0, 0)
Answer: a) (1, 5)
- The equation y = mx + c represents:
- a) Circle
- b) Parabola
- c) Straight line
- d) Ellipse
Answer: c) Straight line
- What is the slope of the line perpendicular to y = 2x + 3?
- a) 2
- b) -2
- c) 1/2
- d) -1/2
Answer: d) -1/2
- If a line passes through points (1, 4) and (3, 4), what is its slope?
- a) 0
- b) 2
- c) Undefined
- d) 1
Answer: a) 0
- What is the distance between points (1, 1) and (4, 5)?
Answer: b) √20
- The line y = -x + 7 passes through which point?
- a) (2, 5)
- b) (3, 4)
- c) (0, 7)
- d) All of the above
Answer: d) All of the above
- If a line has slope 0, what is the nature of the line?
- a) Horizontal
- b) Vertical
- c) Diagonal
- d) Curved
Answer: a) Horizontal
- Which of the following points lies in Quadrant III?
- a) (-3, -5)
- b) (3, -5)
- c) (-3, 5)
- d) (3, 5)
Answer: a) (-3, -5)
- The slope of the line 2x + 3y = 6 is:
- a) 2/3
- b) -2/3
- c) 3/2
- d) -3/2
Answer: b) -2/3
- What is the y-intercept of the line y = 4x - 8?
Answer: b) -8
- The points (2, 3), (4, 6), and (6, 9) are:
- a) Collinear
- b) Not collinear
- c) On a circle
- d) None of the above
Answer: a) Collinear
- Which of the following is true about the slope of parallel lines?
- a) Slopes are equal
- b) Slopes are negative reciprocals
- c) Slopes multiply to zero
- d) Slopes multiply to -1
Answer: a) Slopes are equal
- Find the equation of the line with slope 3 passing through (1, 2).
- a) y = 3x + 2
- b) y - 2 = 3(x - 1)
- c) y = 3(x + 1) + 2
- d) y = 3x - 1
Answer: b) y - 2 = 3(x - 1)
- The slope of the line perpendicular to y = -1/2 x + 4 is:
- a) 2
- b) -2
- c) 1/2
- d) -1/2
Answer: a) 2
- The point (4, -3) lies in which quadrant?
Answer: d) IV
- The length of the line segment between (1, 2) and (1, 5) is:
Answer: a) 3
- Which of the following represents the equation of a circle centered at the origin with radius 5?
- a) x² + y² = 5
- b) x² + y² = 25
- c) (x - 5)² + (y - 5)² = 25
- d) (x + 5)² + (y + 5)² = 25
Answer: b) x² + y² = 25
- The coordinates (0, y) always lie on the:
- a) x-axis
- b) y-axis
- c) Line y = x
- d) Line x = y
Answer: b) y-axis
- What is the slope of the line passing through (0, 0) and (5, 0)?
- a) 0
- b) 1
- c) Undefined
- d) 5
Answer: a) 0
- The equation y = x + 1 has a slope of:
- a) 0
- b) 1
- c) -1
- d) Undefined
Answer: b) 1
- The slope-intercept form of a line is:
- a) y = mx + c
- b) y - y1 = m(x - x1)
- c) Ax + By = C
- d) x = y + c
Answer: a) y = mx + c
- If two points are the same, the distance between them is:
- a) 0
- b) 1
- c) Undefined
- d) Infinite
Answer: a) 0
- The slope of the line y = -3x + 5 is:
Answer: b) -3
- Which of these is NOT a point on the line y = 2x + 1?
- a) (1, 3)
- b) (2, 5)
- c) (3, 7)
- d) (0, 0)
Answer: d) (0, 0)
- The line passing through points (0, 0) and (3, 9) has a slope of:
Answer: a) 3
- Which equation represents a line with zero y-intercept?
- a) y = 2x
- b) y = 2x + 1
- c) y = -3x + 4
- d) y = 4
Answer: a) y = 2x
- The point (5, -2) lies in which quadrant?
Answer: d) IV
- Which of these points lies on the line y = 3x - 1?
- a) (2, 5)
- b) (1, 2)
- c) (0, -1)
- d) All of the above
Answer: d) All of the above
- The slope of the line passing through (3, 7) and (3, 10) is:
- a) 0
- b) Undefined
- c) 1
- d) 3
Answer: b) Undefined
- Which of the following is the distance formula between two points (x1, y1) and (x2, y2)?
- a) √((x2 + x1)² + (y2 + y1)²)
- b) √((x2 - x1)² + (y2 - y1)²)
- c) (x2 - x1) + (y2 - y1)
- d) (x2 + x1) / (y2 + y1)
Answer: b) √((x2 - x1)² + (y2 - y1)²)
- If the slope of a line is 1, the line makes an angle of ______ degrees with the positive x-axis.
- a) 45°
- b) 90°
- c) 60°
- d) 30°
Answer: a) 45°
- The midpoint of points (4, -2) and (10, 6) is:
- a) (7, 2)
- b) (14, 4)
- c) (6, 4)
- d) (3, -4)
Answer: a) (7, 2)
- The graph of y = 4 is:
- a) A vertical line
- b) A horizontal line
- c) A line with slope 4
- d) A curve
Answer: b) A horizontal line
- The slope of a line perpendicular to y = 5x + 2 is:
- a) 5
- b) -1/5
- c) 1/5
- d) -5
Answer: b) -1/5
- The equation of a line with zero slope is:
- a) y = c (constant)
- b) x = c (constant)
- c) y = mx + c where m ≠ 0
- d) None of these
Answer: a) y = c (constant)
- The point (0, 0) is called:
- a) The origin
- b) The intercept
- c) The midpoint
- d) None of these
Answer: a) The origin
- Which of the following points lies on the y-axis?
- a) (0, 5)
- b) (5, 0)
- c) (3, 3)
- d) (-2, 2)
Answer: a) (0, 5)
- The equation x = -3 represents a:
- a) Vertical line
- b) Horizontal line
- c) Line with slope -3
- d) None of these
Answer: a) Vertical line
- The equation y = x represents a line passing through the origin with:
- a) Slope 1
- b) Slope 0
- c) Undefined slope
- d) Slope -1
Answer: a) Slope 1
- In which quadrant is the point (-4, 6) located?
- a) Quadrant I
- b) Quadrant II
- c) Quadrant III
- d) Quadrant IV
Answer: b) Quadrant II
- The line equation y = 0 represents:
- a) x-axis
- b) y-axis
- c) Diagonal line
- d) None of these
Answer: a) x-axis
- The slope of a line passing through points (1, 1) and (2, 3) is:
Answer: b) 2
- What is the distance between points (-1, -1) and (2, 3)?
Answer: c) √20
- The line y = mx + c intersects the y-axis at:
- a) (0, c)
- b) (c, 0)
- c) (m, 0)
- d) (0, m)
Answer: a) (0, c)
- Which of the following points lies on the x-axis?
- a) (4, 0)
- b) (0, 4)
- c) (-3, 2)
- d) (2, -3)
Answer: a) (4, 0)
- The slope of a horizontal line is:
- a) 0
- b) 1
- c) Undefined
- d) Infinite
Answer: a) 0
- The slope of a vertical line is:
- a) 0
- b) Undefined
- c) 1
- d) -1
Answer: b) Undefined
- Find the midpoint of points (-2, 4) and (6, -8).
- a) (2, -2)
- b) (4, -4)
- c) (2, 6)
- d) (4, 2)
Answer: a) (2, -2)
- The slope of the line passing through points (2, 3) and (6, 7) is:
Answer: a) 1
- The equation of the line passing through (0, -2) with slope 5 is:
- a) y = 5x - 2
- b) y = 5x + 2
- c) y = -5x - 2
- d) y = -5x + 2
Answer: a) y = 5x - 2
- The points (1, 4), (2, 6), and (3, 8) are:
- a) Collinear
- b) Not collinear
- c) On a circle
- d) None of these
Answer: a) Collinear
- The equation 3x - 4y = 12 represents a line. What is its slope?
- a) 3/4
- b) -3/4
- c) 4/3
- d) -4/3
Answer: b) -3/4
- The distance between points (0, 0) and (5, 12) is:
Answer: b) 13
- Which of the following is the correct form of the equation of a line passing through (x1, y1) with slope m?
- a) y = mx + c
- b) y - y1 = m(x - x1)
- c) Ax + By = C
- d) y = m(x + x1) + y1
Answer: b) y - y1 = m(x - x1)
- The line x = 7 is:
- a) Vertical line
- b) Horizontal line
- c) Line with slope 7
- d) None of these
Answer: a) Vertical line
- The y-coordinate of the midpoint between (4, 5) and (8, 9) is:
Answer: a) 7
- The equation y = -2x + 3 crosses the y-axis at:
- a) (0, -2)
- b) (0, 3)
- c) (3, 0)
- d) (2, 0)
Answer: b) (0, 3)
- The distance between (3, 4) and (7, 1) is:
Answer: d) √29
- The line y = 0 is the:
- a) x-axis
- b) y-axis
- c) Line with zero slope
- d) Both a and c
Answer: d) Both a and c
- The slope of the line perpendicular to y = 3x + 1 is:
- a) 3
- b) -3
- c) 1/3
- d) -1/3
Answer: d) -1/3
- The points (2, 2) and (5, 6) lie on a line with slope:
Answer: b) 4/3
- The distance between (0, 0) and (7, 24) is:
Answer: a) 25
- The line y = mx + c intercepts the x-axis at:
- a) (0, c)
- b) (-c/m, 0)
- c) (c/m, 0)
- d) (0, -c)
Answer: b) (-c/m, 0)
- The graph of the equation x + y = 0 passes through which quadrant(s)?
- a) I and III
- b) II and IV
- c) I and II
- d) III and IV
Answer: a) I and III
- The equation of a line parallel to y = 2x + 3 and passing through (1, 4) is:
- a) y = 2x + 2
- b) y = 2x + 4
- c) y = 2x + 1
- d) y = -2x + 4
Answer: b) y = 2x + 2
- Which of the following points lies on the line 2x - 3y = 6?
- a) (3, 0)
- b) (0, -2)
- c) (0, 2)
- d) (6, 0)
Answer: a) (3, 0)
- The slope of the line 4x + y = 8 is:
- a) 4
- b) -4
- c) 1/4
- d) -1/4
Answer: d) -4
- The midpoint between points (7, -3) and (-1, 5) is:
- a) (3, 1)
- b) (6, 2)
- c) (4, 2)
- d) (3, -4)
Answer: a) (3, 1)
- If two lines are perpendicular, the product of their slopes is:
- a) 0
- b) 1
- c) -1
- d) Undefined
Answer: c) -1
- Which of the following points lies on the line y = -x + 5?
- a) (2, 3)
- b) (1, 4)
- c) (0, 5)
- d) All of the above
Answer: d) All of the above
- The distance between points (1, 2) and (4, 6) is:
Answer: b) √18
- The point (x, y) lies on the y-axis if:
- a) x = 0
- b) y = 0
- c) x = y
- d) y = 1
Answer: a) x = 0
- The line y = 3 is:
- a) Vertical line
- b) Horizontal line
- c) Line with slope 3
- d) None of these
Answer: b) Horizontal line
- The slope of the line through points (-2, 0) and (2, 4) is:
Answer: b) 1
- Which of the following points lies on the line y = 2x + 1?
- a) (1, 3)
- b) (2, 5)
- c) (0, 1)
- d) All of the above
Answer: d) All of the above
- The equation of the line passing through (0, 0) and (4, 2) is:
- a) y = 1/2 x
- b) y = 2x
- c) y = 4x
- d) y = -1/2 x
Answer: a) y = 1/2 x
- The slope of a line parallel to y = -3x + 7 is:
- a) -3
- b) 3
- c) 0
- d) Undefined
Answer: a) -3
- Two points (x1, y1) and (x2, y2) are said to be collinear if:
- a) The slope between them is zero
- b) The slope between them is undefined
- c) The slope between them is equal
- d) They lie on the same line
Answer: d) They lie on the same line
- Find the distance between points (3, 7) and (6, 11):
Answer: a) 5
- The slope of the line passing through (4, -1) and (-2, 3) is:
- a) -2/3
- b) 2/3
- c) 1/2
- d) -3/2
Answer: b) 2/3
- The equation y = mx + c passes through the origin if:
- a) m = 0
- b) c = 0
- c) m = c
- d) m and c both ≠ 0
Answer: b) c = 0
- The line perpendicular to y = 1/2 x + 4 has slope:
- a) 2
- b) -2
- c) 1/2
- d) -1/2
Answer: b) -2
- The slope-intercept form of a line is:
- a) Ax + By = C
- b) y = mx + c
- c) y - y1 = m(x - x1)
- d) (y - y1)/(x - x1) = m
Answer: b) y = mx + c
- Find the midpoint of points (-3, 2) and (5, 10):
- a) (1, 6)
- b) (2, 8)
- c) (3, 5)
- d) (4, 6)
Answer: a) (1, 6)
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