This is the Multiple Choice Questions Part 1 of the Series in Analytic Geometry: Points, Lines and Circles topics in Engineering Mathematics. In Preparation for the ECE Board Exam make sure to expose yourself and familiarize in each and every questions compiled here taken from various sources including but not limited to past Board Examination Questions in Engineering Mathematics, Mathematics Books, Journals and other Mathematics References.
MCQ Topic Outline included in Mathematics Board Exam Syllabi
- MCQ in Rectangular coordinates system | MCQ in Distance Formula | MCQ in Distance between two points in space | MCQ in Slope of a Line | MCQ in Angle between two lines| MCQ in Distance between a point and a line | MCQ in Distance between two lines | MCQ in Division of line segment | MCQ in Area by coordinates | MCQ in Lines | MCQ in Conic sections | MCQ in Circles
Start Practice Exam Test Questions Part 1 of the Series
Choose the letter of the best answer in each questions.
Problem 1: ECE Board April 1999
The linear distance between โ4 and 17 on the number line is
A. 13
B. 21
C. โ17
D. โ13
Answer: Option B
Solution: Review: Solution for Number 1
Problem 2: EE Board April 1994
Find the distance between A (4, โ3) and B (โ2, 5).
A. 11
B. 9
C. 10
D. 8
Answer: Option C
Solution: Review: Solution for Number 2
Problem 3:
If the distance between points (3, y) and (8, 7) is 13, then y is equal to
A. 5 or โ5
B. 5 or 19
C. 19
D. โ5 or 19
Answer: Option D
Solution: Review: Solution for Number 3
Problem 4:
Find the coordinate of a point equidistant from (1, -6), (5, -6) and (6, -1).
A. (2, -2)
B. (3, -2)
C. (3, -3)
D. (2, -3)
Answer: Option C
Solution: Review: Solution for Number 4
Problem 5: EE Board April 1995
The line segment connecting (x, 6) and (9, y) is bisected by the point (7, 3). Find the values of x and y.
A. 14, 6
B. 33, 12
C. 5, 0
D. 14, 6
Answer: Option C
Solution: Review: Solution for Number 5
Problem 6:
If (-2, -4) is the midpoint of (6, -7) and (x, y), then the values of x and y are
A. x = 2, y = 1
B. x = -10, y = -1
C. x = 10, y = -1
D. x = -8, y = -1
Answer: Option B
Solution: Review: Solution for Number 6
Problem 7: ECE Board November 1998
Determine the coordinates of the point which is three-fifths of the way from the point (2, -5) to the point (-3, 5).
A. (-1, 1)
B. (-2, -1)
C. (-1, -2)
D. (1, -1)
Answer: Option A
Solution: Review: Solution for Number 7
Problem 8: ECE Board April 1998
The segment from (-1, 4) to (2, -2) is extended three times its own length. The terminal point is
A. (11, -24)
B. (-11, -20)
C. (11, -18)
D. (11, -20)
Answer: Option D
Solution: Review: Solution for Number 8
Problem 9:
The points (a, 1), (b, 2) and (c, 3) are collinear. Which of the following is true?
A. c โ b = c โ a
B. c โ b = b โ a
C. c โ a = a โ b
D. c โ a = b โ a
Answer: Option B
Solution: Review: Solution for Number 9
Problem 10:
If the slope of the line connecting the origin and point P is ยพ, find the abscissa of P if its ordinate is 6.
A. 2
B. 6
C. 7
D. 8
Answer: Option D
Solution: Review: Solution for Number 10
Problem 11: ECE Board April 1999
Find the inclination of the line passing through (-5, 3) and (10, 7).
A. 14.73
B. 14.93
C. 14.83
D. 14.63
Answer: Option B
Solution: Review: Solution for Number 11
Problem 12:
Find the angle formed by the lines 2x + y โ 8 = 0 and x + 3y + 4 = 0.
A. 30ยฐ
B. 35ยฐ
C. 45ยฐ
D. 60ยฐ
Answer: Option C
Solution: Review: Solution for Number 12
Problem 13:
Find the angle between the lines 3x + 2y = 6 and x + y = 6.
A. 12ยฐ 20โ
B. 11ยฐ 19โ
C. 14ยฐ 25โ
D. 13ยฐ 06โ
Answer: Option B
Solution: Review: Solution for Number 13
Problem 14:
What is the acute angle between the lines y = 3x + 2 and y = 4x + 9?
A. 4.4ยฐ
B. 28.3ยฐ
C. 5.2ยฐ
D. 18.6ยฐ
Answer: Option A
Solution: Review: Solution for Number 14
Problem 15: EE Board October 1997
Find the distance of the line 3x + 4y = 5 from the origin.
A. 4
B. 3
C. 2
D. 1
Answer: Option D
Solution: Review: Solution for Number 15
Problem 16: CE Board November 1992
The two points on the lines 2x = 3y + 4 = 0 which are at a distance 2 from the line 3x + 4y โ 6 = 0 are?
A. (-5, 1) and (-5, 2)
B. (64, -44) and (4, -4)
C. (8, 8) and (12, 12)
D. (44, -64) and (-4, 4)
Answer: Option B
Solution: Review: Solution for Number 16
Problem 17: CE Board November 1992
The distance from the point (2, 1) to the line 4x โ 3y + 5 = 0 is?
A. 1
B. 2
C. 3
D. 4
Answer: Option B
Solution: Review: Solution for Number 17
Problem 18: CE Board November 1996
Determine the distance from (5, 10) to the line x โ y = 0.
A. 3.33
B. 3.54
C. 4.23
D. 5.45
Answer: Option B
Solution: Review: Solution for Number 18
Problem 19:
The distance from a point (1, 3) to the line 4x + 3y + 12 = 0 is
A. 4 units
B. 5 units
C. 6 units
D. 7 units
Answer: Option B
Solution: Review: Solution for Number 19
Problem 20: CE Board May 1992
Find the distance between the given lines 4x โ 3y = 12 and 4x โ 3y = -8.
A. 3
B. 4
C. 5
D. 6
Answer: Option B
Solution: Review: Solution for Number 20
Problem 21: EE Board April 1995
Find the distance between the lines, 3x + y โ 12 = 0 and 3x + y โ 4 = 0.
A. 16/โ10
B. 12/โ10
C. 4/โ10
D. 8/โ10
Answer: Option D
Solution: Review: Solution for Number 21
Problem 22: ME Board October 1996
What is the length of the line with a slope of 4/3 from a point (6, 4) to the y-axis?
A. 10
B. 25
C. 50
D. 75
Answer: Option A
Solution: Review: Solution for Number 22
Problem 23: ME Board April 1998
Find the slope of the line defined by y โ x = 5.
A. 1
B. 1/4
C. -1/2
D. 5 + x
Answer: Option A
Solution: Review: Solution for Number 23
Problem 24: CE Board November 1995
What is the slope of the line 3x + 2y + 1 = 0?
A. 3/2
B. 2/3
C. -3/2
D. -2/3
Answer: Option C
Solution: Review: Solution for Number 24
Problem 25: ECE Board November 1990
In a Cartesian coordinates, the vertices of a triangle are defined by the following points: (-2, 0) and (3, 3). What is the area?
A. 8 sq. units
B. 9 sq. units
C. 10 sq. units
D. 11 sq. units
Answer: Option B
Solution: Review: Solution for Number 25
Problem 26: EE Board April 1994
Given three vertices of a triangle whose coordinates are A (1, 1), B (3, -3) and (5, -3). Find the area of the triangle.
A. 3
B. 4
C. 5
D. 6
Answer: Option B
Solution: Review: Solution for Number 26
Problem 27: ECE Board November 1990
In a Cartesian coordinates, the vertices of a square are: (1, 1), (0, 8), (4, 5) and (-3, 4). What is the area?
A. 20 sq. units
B. 30 sq. units
C. 25 sq. units
D. 35 sq. units
Answer: Option C
Solution: Review: Solution for Number 27
Problem 28: EE Board April 1997
A line passes thru (1, -3) and (-4, 2). Write the equation of the line in slope-intercept form.
A. y โ 4 = x
B. y = -x โ 2
C. y = x โ 4
D. y โ 2 = x
Answer: Option B
Solution: Review: Solution for Number 28
Problem 29: EE Board October 1997
What is the x-intercept of the line passing through (1, 4) and (4, 1)?
A. 4.5
B. 5
C. 4
D. 6
Answer: Option B
Solution: Review: Solution for Number 29
Problem 30: ME Board April 1997
Find the equation of the straight line with a slope of 3 and a y-intercept of 1.
A. 3x + y โ 1 = 0
B. 3x โ y + 1 = 0
C. x + 3y + 1 = 0
D. x โ 3y โ 1 = 0
Answer: Option B
Solution: Review: Solution for Number 30
Problem 31: ECE Board April 1999
If the points (-2, 3), (x, y) and (-3, 5) lie on a straight line, then the equation of the line is _______.
A. x โ 2y โ 1 = 0
B. 2x + y โ 1 = 0
C. x + 2y โ 1 = 0
D. 2x + y + 1 = 0
Answer: Option D
Solution: Review: Solution for Number 31
Problem 32: ME Board April 1998
The equation of a line that intercepts the x-axis at x = 4 and the y-axis at y = -6 is,
A. 3x + 2y = 12
B. 2x โ 3y = 12
C. 3x โ 2y = 12
D. 2x โ 3y = 12
Answer: Option C
Solution: Review: Solution for Number 32
Problem 33:
A line with an inclination of 45ยบ passes through (-5/2, -9/2). What is the x-coordinate of a point on the line if its corresponding y-coordinate is 6?
A. 6
B. 7
C. 8
D. 9
Answer: Option C
Solution: Review: Solution for Number 33
Problem 34:
Find the equation of the line passing through the origin and with a slope of 6?
A. y โ 6x = 0
B. y = -6
C. x + y = -6
D. 6x + y = 0
Answer: Option A
Solution: Review: Solution for Number 34
Problem 35:
Find the equation of the line if the x-intercept and y-intercept are -2 and 4, respectively.
A. y โ 2x โ 4 = 0
B. y + 2x โ 4 = 0
C. y โ 2x + 4 = 0
D. y + 2x + 4 = 0
Answer: Option B
Solution: Review: Solution for Number 35
Problem 36: ECE Board April 1998
Determine B such that 3x + 2y โ 7 = 0 is perpendicular to 2x โ By + 2 = 0.
A. 5
B. 4
C. 3
D. 2
Answer: Option C
Solution: Review: Solution for Number 36
Problem 37:
The line 2x โ 3y + 2 = 0 is perpendicular to another line L1 of unknown equation. Find the slope of L1.
A. 3/2
B. -3/2
C. 2/3
D. -2/3
Answer: Option B
Solution: Review: Solution for Number 37
Problem 38:
A line through (-5, 2) and (1, -4) is perpendicular to the line through (x, -7) and (8, 7). Find the x.
A. -4
B. -5
C. -6
D. -19/3
Answer: Option C
Solution: Review: Solution for Number 38
Problem 39: CE Board May 1996
What is the equation of the line that passes thru (4, 0) and is parallel to the line x โ y โ 2 = 0?
A. x โ y + 4 = 0
B. x + y + 4 = 0
C. x โ y โ 4 = 0
D. x โ y = 0
Answer: Option C
Solution: Review: Solution for Number 39
Problem 40:
Find the equation of the line through point (3, 1) and is perpendicular to the line x + 5y +5 = o.
A. 5x โ 2y = 14
B. 5x โ y = 14
C. 2x โ 5y = 14
D. 2x + 5y = 14
Answer: Option B
Solution: Review: Solution for Number 40
Problem 41:
Find the equation of the perpendicular bisector of the line joining (5, 0) and (-7, 3).
A. 8x + 2y + 11 = 0
B. 8x โ 2y + 11 = 0
C. 8x โ y + 11 = 0
D. 8x + y + 11 = 0
Answer: Option B
Solution: Review: Solution for Number 41
Problem 42:
Which of the following lines is parallel to the line 3x โ 2y + 6 = 0?
A. 3x + 2y โ 12 = 0
B. 4x โ 9y = 6
C. 12x + 18y = 15
D. 15 x โ 10y โ 9 = 0
Answer: Option D
Solution: Review: Solution for Number 42
Problem 43:
The equation of the line through (-3, -5) parallel to 7x + 2y โ 4 = 0 is
A. 7x + 2y + 31 = 0
B. 7x โ 2y + 30 = 0
C. 7x โ 2y โ 4 = 0
D. 2x + 7y + 30 = 0
Answer: Option A
Solution: Review: Solution for Number 43
Problem 44:
What is the equation of the line joining the points (3, -2) and (-7, 6)?
A. 2x + 3y = 0
B. 4x โ 5y = 22
C. 4x + 5y = 2
D. 5x + 4y = 7
Answer: Option C
Solution: Review: Solution for Number 44
Problem 45:
What is the equation of the line passing through (-2, 6) with the x-intercept half the y-intercept?
A. x โ y = 6
B. 2x + 2y + 2 = 0
C. 3x โ y + 2 = 0
D. 2x + y โ 2 = 0
Answer: Option D
Solution: Review: Solution for Number 45
Problem 46: CE Board May 1997
Find the slope of a line having a parametric equation of x = 2 + t and y = 5 โ 3t.
A. 2
B. 3
C. -2
D. -3
Answer: Option D
Solution: Review: Solution for Number 46
Problem 47: CE Board May 1998
Find the slope of the line having a parametric equation y = 4t + 6 and x = t + 1.
A. 1
B. 2
C. 3
D. 4
Answer: Option D
Solution: Review: Solution for Number 47
Problem 48: ECE Board April 1999
Two vertices of a triangle are (2, 4) and (-2, 3) and the area is 2 square units, the locus of the third vertex is?
A. 4x โ y = 14
B. 4x + 4y = 14
C. x + 4y = 12
D. x โ 4y = -14
Answer: Option D
Solution: Review: Solution for Number 48
Problem 49: ECE Board April 1998
Find the area of the triangle which the line 2x โ 3y + 6 = 0 forms with the coordinate axis.
A. 3
B. 4
C. 5
D.2
Answer: Option A
Solution: Review: Solution for Number 49
Problem 50: ECE Board November 1998
A line passes through point (2, 2). Find the equation of the line if the length of the line segment intercepted by the coordinate axes is the square root of 5.
A. 2x + y โ 2 = 0
B. 2x โ y โ 2 = 0
C. 2x โ y + 2 = 0
D. 2x + y + 2 = 0
Answer: Option B
Solution: Review: Solution for Number 50
Online Questions and Answers in Analytic Geometry: Points, Lines and Circles Series
Following is the list of practice exam test questions s in this brand new series:
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I think sa question number 35 ang answer po ay letter A. y-2x-4=0. Pacheck na lang po. Thank you !