Geometry • Coordinate Geometry Practice Drills (67 Qs)• Official Answer Keys

CAT Coordinate Geometry & Lines Practice Questions (65+ Questions)

Slope of Lines, Perpendicular and Parallel Lines, Distance Formula, Section Formula, and Area of Polygons in 2D Plane

67 Total Questions

MCQ: 53 (+3 / -1)

TITA: 14 (0 Negative Penalty)

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Official Exam Fact Sheet & Direct Answer Snapshot

Fact-Checked Archive

CAT Coordinate Geometry & Lines Practice Questions (65+ Questions): This official paper archive contains 67 verified CAT questions curated directly from IIM convenor response sheets. The marking scheme follows standard CAT rules: +3 marks for correct MCQs, -1 mark for incorrect MCQs, and zero negative marking penalty for 14 TITA questions. All solutions provide step-by-step mathematical derivations, official convenor response keys, and full 1:1 TCS iON CBT simulator compatibility.

Curriculum DomainCAT Geometry

Target Solving Speed1.5 to 2.0 mins / question

Exam Weightage1 Question in QA

Testing PlatformTCS iON CBT Simulator

Audited & Verified by ThinkCAT Academic & Editorial Council (Lead: Balaji Rao, IIM Alumnus)Response Sheet Master Key Mapped

Core Formulas & Shortcut Matrix: Coordinate Geometry Practice Drills

Verified LaTeX Theorems

Perpendicular Distance to LineFormula #1

d = \frac{|Ax_1 + By_1 + C|}{\ \

\sqrt{A^2 + B^2}

}

Distance from point (x1, y1) to line Ax + By + C = 0.

Slope Product for Perpendicular LinesFormula #2

m_1 × m_2 = -1

For parallel lines: m1 = m2.

Exam Hall Traps & Speedbreakers to Avoid

•Forgetting the absolute value in perpendicular distance or coordinate area formulas.

Bite-Sized Practice Sets (8 Modules Available)

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Difficulty: Moderate

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Difficulty: Hard

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Difficulty: Hard

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Official Exam Questions & Explanations (25 of 67)

Sorted in official convenor sequence

Question 1 of 67

ThinkCAT Practice SetQAGeometry • Straight LinesEasy

What is the equation of the line passing through the points

(2, 3)

and

(4, 7)

Practice More Questions

Official Convenor Answer Key: A

Verified Solution: Slope of the line is

\frac{7-3}{4-2} = 2

. Using point-slope form with

(2,3) , we get

y - 3 = 2(x - 2) ⇒ y = 2x - 1 + 3 ⇒ y = 2x + 1$.

Question 2 of 67

ThinkCAT Practice SetQAGeometry • Straight LinesModerate

What is the $y - intercept of the line $3x - 4y = 12$?

Practice More Questions

Official Convenor Answer Key: A

Verified Solution: Rewrite the equation in slope-intercept form: - 4y = -3x + 12 ⇒ y =

\frac{7-3}{4-2} = 2

x - 3

. The $y - intercept is - 3$.

Question 3 of 67

ThinkCAT Practice SetQAGeometry • Straight LinesHard

Find the equation of the line perpendicular to

2x - 3y = 6

and passing through

(1, 4)

Practice More Questions

Official Convenor Answer Key: A

Verified Solution: The slope of

\frac{7-3}{4-2} = 2

\frac{2}{3}

. The slope of the perpendicular line is -

\frac{3}{2}

$. Using point-slope form with $(1, 4) , we get

y - 4 = - \frac{3}{2}

(x - 1) ⇒ 2y - 8 = -3x + 3 ⇒ 3x + 2y = 11$.

Question 4 of 67

ThinkCAT Practice SetQAGeometry • Straight LinesEasy

What is the $x - intercept of the line $y = 4x - 8$?

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Official Convenor Answer Key: B

Verified Solution: To find the

\frac{7-3}{4-2} = 2

y = 0

. So, &#36;0 = 4x - 8 \Rightarrow x = 2

Question 5 of 67

ThinkCAT Practice SetQAGeometry • Straight LinesModerate

Find the equation of the line passing through

(2, -1)

and parallel to

3x - 2y = 5

TITA Answer:

Practice More Questions

Official Convenor Answer Key: 3x - 2y = 8

Verified Solution: The slope of

\frac{7-3}{4-2} = 2

\frac{2}{3}

. Using point-slope form with

\frac{3}{2}

(2 - x) ⇒ -2y - 2 = 3(2 - x) ⇒ 3x - 2y = 8$.

Question 6 of 67

ThinkCAT Practice SetQAGeometry • Straight LinesHard

What is the $x - intercept of the line $y = -x + 5$?

Practice More Questions

Official Convenor Answer Key: B

Verified Solution: To find the

\frac{7-3}{4-2} = 2

y = 0

. So, &#36;0 = 4x - 8 \Rightarrow x = 2

Question 7 of 67

ThinkCAT Practice SetQAGeometry • Straight LinesEasy

What is the slope of the line

4y = 8x + 12

Practice More Questions

Official Convenor Answer Key: B

Verified Solution: Rewrite the equation in slope-intercept form:

\frac{7-3}{4-2} = 2

. The slope is

2

Question 8 of 67

ThinkCAT Practice SetQAGeometry • Straight LinesEasy

The equation of a straight line is

y = 2x + 3

. What is the slope of this line?

Practice More Questions

Official Convenor Answer Key: B

Verified Solution: The equation of the line is in the slope-intercept form

\frac{7-3}{4-2} = 2

m$ is the slope. Here, $m = 2$. Therefore, the slope is 2.

Question 9 of 67

ThinkCAT Practice SetQAGeometry • Straight LinesModerate

If the lines

y = 3x + 2

and

y = -x + 5

intersect, what is the $x - coordinate of the intersection point?

Practice More Questions

Official Convenor Answer Key: A

Verified Solution: Set the equations equal to find the intersection:

\frac{7-3}{4-2} = 2

. Solving for

x

gives

4x = 3 , so

x =

\frac{3}{4}

≈ 0.75$. The closest option is 1.

Question 10 of 67

ThinkCAT Practice SetQAGeometry • Straight LinesHard

If the lines

2x - 3y = 6

and

4x + 6y = -12

are graphed, what is the relationship between them?

Practice More Questions

Official Convenor Answer Key: C

Verified Solution: Simplify the second equation to

\frac{7-3}{4-2} = 2

. Both equations have the same slope, indicating they are either parallel or coincident. Checking, they are multiples of each other, so they are coincident.

Question 11 of 67

ThinkCAT Practice SetQAGeometry • Straight LinesEasy

What is the slope of the line

y = -2x + 7

TITA Answer:

Practice More Questions

Official Convenor Answer Key: -2

Verified Solution: The equation is in the form

\frac{7-3}{4-2} = 2

m$ is the slope. Here, $m = -2$.

Question 12 of 67

ThinkCAT Practice SetQAGeometry • Straight LinesModerate

If the lines

y = \frac{1}{2}

x + 3$ and $y = -2x + 1$ intersect, what is the $y - coordinate of the intersection point?

Practice More Questions

Official Convenor Answer Key: C

Verified Solution: Set the equations equal to find the intersection:

\frac{7-3}{4-2} = 2

. Solving for

x

gives

\frac{5}{2}x = -2 , so

x = -

\frac{4}{5}

. Substituting back,

y =

\frac{1}{2}

× -

\frac{4}{5}

+ 3 = 2.8 ≈ 3$.

Question 13 of 67

ThinkCAT Practice SetQAGeometry • Straight LinesHard

If the lines

3x - 2y = 6

and

6x - 4y = 12

are graphed, what is the relationship between them?

Practice More Questions

Official Convenor Answer Key: C

Verified Solution: Simplify the second equation to

\frac{7-3}{4-2} = 2

. Both equations are identical, indicating they are coincident.

Question 14 of 67

ThinkCAT Practice SetQAGeometry • Straight LinesModerate

If the equation of a line is $y = 3x + 5 , what is the slope of the line?

Practice More Questions

Official Convenor Answer Key: B

Verified Solution: The slope of a line given by the equation

\frac{7-3}{4-2} = 2

2

. Therefore, the slope of the line

y = 3x + 5

3

Question 15 of 67

ThinkCAT Practice SetQAGeometry • Straight LinesModerate

What is the $y - intercept of the line given by the equation $2x - 3y = 6$?

Practice More Questions

Official Convenor Answer Key: A

Verified Solution: To find the

\frac{7-3}{4-2} = 2

x = 0$ and solve for $y

. So, &#36;0 = 4x - 8 \Rightarrow x = 2

2(0) - 3y = 6 ⇒ y = -2$.

Question 16 of 67

ThinkCAT Practice SetQAGeometry • Straight LinesModerate

What is the slope of the line passing through points

(3, 4)

and

(7, 10)

TITA Answer:

Practice More Questions

Official Convenor Answer Key: 1.5

Verified Solution: The slope of a line passing through two points

\frac{7-3}{4-2} = 2

and

(x_2, y_2)

is given by

\frac{y_2 - y_1}{x_2 - x_1}

. So, the slope is

\frac{10 - 4}{7 - 3} = \frac{6}{4} = 1.5

Question 17 of 67

ThinkCAT Practice SetQAGeometry • Straight LinesModerate

What is the equation of the line perpendicular to

y = 2x + 3

and passing through the point

(1, 2)

Practice More Questions

Official Convenor Answer Key: B

Verified Solution: The slope of the given line is 2. The slope of the perpendicular line is -

\frac{7-3}{4-2} = 2

$. Using the point-slope form, $y - 2 = -

2

$(x - 1) , simplifies to $y = -

\frac{1}{2}

x + \frac{5}{2}

Question 18 of 67

ThinkCAT Practice SetQAGeometry • Straight LinesModerate

If the line

2x - 3y + 6 = 0

is reflected over the line $y = x , what is the equation of the reflected line?

Practice More Questions

Official Convenor Answer Key: A

Verified Solution: Reflecting a line over

\frac{7-3}{4-2} = 2

swaps the

x

and

x - 3

terms. Thus, the equation becomes $2y - 3x + 6 = 0 , or rearranged, $3x - 2y - 6 = 0$.

Question 19 of 67

ThinkCAT Practice SetQAGeometry • Straight LinesModerate

Find the distance between the points

(3, 4)

and

(7, 9)

TITA Answer:

Practice More Questions

Official Convenor Answer Key: \sqrt{29}

Verified Solution: The distance between two points

\frac{7-3}{4-2} = 2

and

(x_2, y_2)

is given by

\frac{y_2 - y_1}{x_2 - x_1}

. Plugging in the coordinates, we get

\sqrt{(7 - 3)^2 + (9 - 4)^2} = \sqrt{4^2 + 5^2} = \sqrt{16 + 25} = \sqrt{41}

Question 20 of 67

ThinkCAT Practice SetQAGeometry • Straight LinesEasy

If the line

y = 2x + 3

passes through the point $(a, 7) , what is the value of $a$?

Practice More Questions

Official Convenor Answer Key: B

Verified Solution: Substitute

\frac{7-3}{4-2} = 2

into the equation

x

. We get $7 = 2a + 3

. Solving for

a , we get

a = 2

. Hence, the correct answer is B.

Question 21 of 67

ThinkCAT Practice SetQAGeometry • Straight LinesModerate

What is the x-intercept of the line

3x - 4y + 12 = 0

Practice More Questions

Official Convenor Answer Key: A

Verified Solution: To find the x-intercept, set

\frac{7-3}{4-2} = 2

. So,

x

. Solving for

. Solving for

x = -4$. Hence, the correct answer is A.

Question 22 of 67

ThinkCAT Practice SetQAGeometry • Straight LinesEasy

If the line

y = 2x + 3

intersects the y-axis at point A, what are the coordinates of point A?

TITA Answer:

Practice More Questions

Official Convenor Answer Key: (0, 3)

Verified Solution: The y-intercept of a line is the point where the line crosses the y-axis. At the y-axis,

\frac{7-3}{4-2} = 2

. Substituting

x

into the equation

y = 2x + 3

gives

y = 3

. Therefore, the coordinates of point A are

(0, 3)

Question 23 of 67

ThinkCAT Practice SetQAGeometry • Straight LinesModerate

What is the slope of the line passing through the points

(2, 3)

and

(5, 9)

1B) 2C) 3D)

4

Practice More Questions

Official Convenor Answer Key: B

Verified Solution: The slope of a line passing through points

\frac{7-3}{4-2} = 2

and

(x_2, y_2)

is given by the formula

\frac{y_2 - y_1}{x_2 - x_1}

. Substituting the given points, we get

m = \frac{9 - 3}{5 - 2} = \frac{6}{3} = 2

Question 24 of 67

ThinkCAT Practice SetQAGeometry • Straight LinesHard

Find the x-coordinate of the point of intersection of the lines

y = 2x + 3

and

y = -x + 5

TITA Answer:

Practice More Questions

Official Convenor Answer Key: \frac{2}{3}

Verified Solution: To find the point of intersection, set the equations equal to each other:

\frac{7-3}{4-2} = 2

. Solving for

x

3x = 2 , so

x = \frac{2}{3}

. The x-coordinate of the point of intersection is

\frac{2}{3}

Question 25 of 67

ThinkCAT Practice SetQAGeometry • Straight LinesEasy

If the line

y = 3x - 4

intersects the x-axis at point B, what are the coordinates of point B?

TITA Answer:

Practice More Questions

Official Convenor Answer Key: (\frac{4}{3}, 0)

Verified Solution: The x-intercept of a line is the point where the line crosses the x-axis. At the x-axis,

\frac{7-3}{4-2} = 2

. Substituting

x

into the equation

y = 2x + 3

gives

y = 3

. Solving for

x , we get

x =

\frac{4}{5}

$. Therefore, the coordinates of point B are $(

\frac{4}{3}

, 0).

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Frequently Asked Questions about CAT Coordinate Geometry & Lines Practice Questions (65+ Questions)

What concepts are covered in the Coordinate Geometry Practice Drills practice module?

This module covers Straight Lines with 67 verified problems ranging from core foundation to high-difficulty CAT exam hall level.

What is the recommended solving time for Coordinate Geometry Practice Drills questions?

The ideal target pace is 1.5 to 2.0 mins / question. Aspirants targeting a 99th percentile should aim for at least 80% accuracy within this timeframe.

Where can I find official past year CAT papers for Coordinate Geometry Practice Drills?

Official past year exam questions are available in our CAT Geometry PYQ Hub module.

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CAT Coordinate Geometry & Lines Practice Questions (65+ Questions)

Core Formulas & Shortcut Matrix: Coordinate Geometry Practice Drills

Bite-Sized Practice Sets (8 Modules Available)

Set 01: Straight Lines

Set 02: Straight Lines

Set 03: Straight Lines

Set 04: Straight Lines

Set 05: Straight Lines

Set 06: Straight Lines

Set 07: Straight Lines

Set 08: Straight Lines

Attempt under official TCS iON 40-Min countdown timer

Official Exam Questions & Explanations (25 of 67)

+ 42 More Official Questions in this Bank

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Frequently Asked Questions about CAT Coordinate Geometry & Lines Practice Questions (65+ Questions)

What concepts are covered in the Coordinate Geometry Practice Drills practice module?

What is the recommended solving time for Coordinate Geometry Practice Drills questions?

Where can I find official past year CAT papers for Coordinate Geometry Practice Drills?

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