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.

### Multiple Choice Questions Topic Outline

- MCQs in Rectangular coordinates system | MCQs in Distance Formula | MCQs in Distance between two points in space | MCQs in Slope of a Line | MCQs in Angle between two lines| MCQs in Distance between a point and a line | MCQs in Distance between two lines | MCQs in Division of line segment | MCQs in Area by coordinates | MCQs in Lines | MCQs in Conic sections | MCQs in Circles

### Online Questions and Answers in Analytic Geometry: Points, Lines and Circles Series

Following is the list of multiple choice questions in this brand new series:

**Analytic Geometry: Points, Lines and Circles MCQs**

**MCQs from Number 1 – 50**Answer key:

**PART I**

**MCQs from Number 51 – 100**Answer key:

**PART II**

### Start Practice Exam Test Questions Part I 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. 30º
- B. 35º
- C. 45º
- D. 60º

**Problem 13:**

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

- A. 12º 20’
- B. 11º 19’
- C. 14º 25’
- D. 13º 06’

**Problem 14:**

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

- A. 4.4º
- B. 28.3º
- C. 5.2º
- D. 18.6º

**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.

**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