MCQ in Analytic Geometry: Points, Lines and Circles Part 1 | Math Board Exam

MCQ in Analytic Geometry: Points, Lines and Circles Part 1 | Mathematics Board Exam Practice

Analytic geometry is where algebra and geometry meet, and that intersection is exactly what makes it one of the more interesting and more demanding topics in the Mathematics section of the board exam. Points, lines and circles form the foundation of this subject, and if that foundation is shaky, everything that comes after it becomes harder than it needs to be.

This is Part 1 of the Analytic Geometry MCQ Series on Pinoybix, focused specifically on points, lines and circles. Every question here was compiled from past board exam problems, engineering mathematics textbooks, academic journals, and other references that have helped engineering students and reviewees prepare for the Mathematics board exam over the years.

Work through each item with care. Analytic geometry problems have a way of looking straightforward until you realize the question is testing something more specific than you initially noticed. Read every problem completely before setting up your solution, and make sure you understand what is actually being asked before you start computing.

If this is your first time going through this topic in your review, take it at a pace that lets you actually absorb the concepts. Getting through the set fast means nothing if the understanding does not come with it. Note every item that slows you down. Those are the ones worth spending the most time on.

Start here, build the foundation, and carry that into the rest of the series.

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 –4 and 17 on the number line is

A. 13

B. 21

C. –17

D. –13

Problem 2: EE Board April 1994

Find the distance between A (4, –3) and B (–2, 5).

A. 11

B. 9

C. 10

D. 8

Problem 3:

If the distance between points (3, y) and (8, 7) is 13, then y is equal to

A. 5 or –5

B. 5 or 19

C. 19

D. –5 or 19

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)

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

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

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)

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)

Problem 9:

The points (a, 1), (b, 2) and (c, 3) are collinear. Which of the following is true?

A. c – b = c – a

B. c – b = b – a

C. c – a = a – b

D. c – a = b – a

Problem 10:

If the slope of the line connecting the origin and point P is ¾, find the abscissa of P if its ordinate is 6.

A. 2

B. 6

C. 7

D. 8

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°

Problem 12:

Find the angle formed by the lines 2x + y – 8 = 0 and x + 3y + 4 = 0.

A. 30°

B. 35°

C. 45°

D. 60°

Problem 13:

Find the angle between the lines 3x + 2y = 6 and x + y = 6.

A. 12° 20’

B. 11° 19’

C. 14° 25’

D. 13° 06’

Problem 14:

What is the acute angle between the lines y = 3x + 2 and y = 4x + 9?

A. 4.4°

B. 28.3°

C. 5.2°

D. 18.6°

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

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 – 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)

Problem 17: CE Board November 1992

The distance from the point (2, 1) to the line 4x – 3y + 5 = 0 is?

A. 1

B. 2

C. 3

D. 4

Problem 18: CE Board November 1996

Determine the distance from (5, 10) to the line x – y = 0.

A. 3.33

B. 3.54

C. 4.23

D. 5.45

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

Problem 20: CE Board May 1992

Find the distance between the given lines 4x – 3y = 12 and 4x – 3y = -8.

A. 3

B. 4

C. 5

D. 6

Problem 21: EE Board April 1995

Find the distance between the lines, 3x + y – 12 = 0 and 3x + y – 4 = 0.

A. 16/√10

B. 12/√10

C. 4/√10

D. 8/√10

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

Problem 23: ME Board April 1998

Find the slope of the line defined by y – x = 5.

A. 1

B. 1/4

C. -1/2

D. 5 + x

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

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

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

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

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 – 4 = x

B. y = -x – 2

C. y = x – 4

D. y – 2 = x

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

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 – 1 = 0

B. 3x – y + 1 = 0

C. x + 3y + 1 = 0

D. x – 3y – 1 = 0

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 – 2y – 1 = 0

B. 2x + y – 1 = 0

C. x + 2y – 1 = 0

D. 2x + y + 1 = 0

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 – 3y = 12

C. 3x – 2y = 12

D. 2x – 3y = 12

Problem 33:

A line with an inclination of 45º 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

Problem 34:

Find the equation of the line passing through the origin and with a slope of 6?

A. y – 6x = 0

B. y = -6

C. x + y = -6

D. 6x + y = 0

Problem 35:

Find the equation of the line if the x-intercept and y-intercept are -2 and 4, respectively.

A. y – 2x – 4 = 0

B. y + 2x – 4 = 0

C. y – 2x + 4 = 0

D. y + 2x + 4 = 0

Problem 36: ECE Board April 1998

Determine B such that 3x + 2y – 7 = 0 is perpendicular to 2x – By + 2 = 0.

A. 5

B. 4

C. 3

D. 2

Problem 37:

The line 2x – 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

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

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 – y – 2 = 0?

A. x – y + 4 = 0

B. x + y + 4 = 0

C. x – y – 4 = 0

D. x – y = 0

Problem 40:

Find the equation of the line through point (3, 1) and is perpendicular to the line x + 5y +5 = o.

A. 5x – 2y = 14

B. 5x – y = 14

C. 2x – 5y = 14

D. 2x + 5y = 14

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 – 2y + 11 = 0

C. 8x – y + 11 = 0

D. 8x + y + 11 = 0

Problem 42:

Which of the following lines is parallel to the line 3x – 2y + 6 = 0?

A. 3x + 2y – 12 = 0

B. 4x – 9y = 6

C. 12x + 18y = 15

D. 15 x – 10y – 9 = 0

Problem 43:

The equation of the line through (-3, -5) parallel to 7x + 2y – 4 = 0 is

A. 7x + 2y + 31 = 0

B. 7x – 2y + 30 = 0

C. 7x – 2y – 4 = 0

D. 2x + 7y + 30 = 0

Problem 44:

What is the equation of the line joining the points (3, -2) and (-7, 6)?

A. 2x + 3y = 0

B. 4x – 5y = 22

C. 4x + 5y = 2

D. 5x + 4y = 7

Problem 45:

What is the equation of the line passing through (-2, 6) with the x-intercept half the y-intercept?

A. x – y = 6

B. 2x + 2y + 2 = 0

C. 3x – y + 2 = 0

D. 2x + y – 2 = 0

Problem 46: CE Board May 1997

Find the slope of a line having a parametric equation of x = 2 + t and y = 5 – 3t.

A. 2

B. 3

C. -2

D. -3

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

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 – y = 14

B. 4x + 4y = 14

C. x + 4y = 12

D. x – 4y = -14

Problem 49: ECE Board April 1998

Find the area of the triangle which the line 2x – 3y + 6 = 0 forms with the coordinate axis.

A. 3

B. 4

C. 5

D.2

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 – 2 = 0

B. 2x – y – 2 = 0

C. 2x – y + 2 = 0

D. 2x + y + 2 = 0

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: