The area of the triangle with vertices (0,0), (4,0), (0,6) is:
- 10
- 12
- 14
- 24
Show answer and explanation
Answer: B. 12
Area=½(4)(6)=12.
FSC Mathematics: Introduction to Analytic Geometry, questions with answers
Practise 28 real Federal Board questions on Introduction to Analytic Geometry from 2023 to 2026. See the answer and explanation as soon as you answer.
28real questions
12multiple choice
5exam sessions
About Introduction to Analytic Geometry in FSC Mathematics
Introduction to Analytic Geometry is one of the 14 main chapters in our Federal Board FSC Mathematics question bank (12th class), and about 6% of its real questions come from it. Tayyari Karo has 28 real questions on this chapter from 2023 to 2026; 12 are multiple choice and marked instantly, and the rest are short and long questions with a model answer. By difficulty: 14 medium, 9 easy, 5 hard.
Work through the questions below, then open the explanation for each one. Redo the ones you missed a few days later.
Try 8 real questions
These are real past-paper questions. Think of your answer first, then open the explanation.
If A(−5,5), B(2,0) and C(0,−2) are vertices of a triangle then its centroid is:
- (1,1)
- (−1,−1)
- (1,−1)
- (−1,1)
Show answer and explanation
Answer: D. (−1,1)
Centroid = ((−5+2+0)/3,(5+0−2)/3) = (−1,1).
What are the coordinates of a point dividing line segment joining O(0,0) and P(6,0) internally in ratio 2:1?
- (0,4)
- (4,4)
- (2,0)
- (4,0)
Show answer and explanation
Answer: D. (4,0)
Section formula: ((2·6+1·0)/3,0) = (4,0).
For what value of k, is the line πx+√2y+√7=0 perpendicular to the line kx+3y+2=0?
- 3/π
- 3√2/π
- −3√2/π
- √2/π
Show answer and explanation
Answer: C. −3√2/π
Slopes: −π/√2 and −k/3. Perpendicular ⇒ product = −1: (π/√2)(k/3)=1 ⇒ k = 3√2/π with a sign giving k=−3√2/π.
If the lines 3x−y−2=0, 5x+αy−3=0 and 2x+y−2=0 are concurrent, then what is the value of α?
- −1
- −2
- −3
- −4
Show answer and explanation
Answer: C. −3
Solving the first and third lines gives their intersection point, which substituted into the second line determines α.
What is the distance of the origin O(0,0) from the line 3x + 4y − 25 = 0?
- 25
- √25
- 5
- 1/√25
Show answer and explanation
Answer: C. 5
Distance = |3(0)+4(0)−25|/√(3²+4²) = 25/5 = 5.
For the homogeneous equation 3x²−5xy+2y²=0: (a) State whether it represents a pair of lines through the origin. (b) Find the individual line equations.
Show model answer
(a) Yes — a homogeneous 2nd-degree equation with real, distinct linear factors always represents a pair of straight lines through the origin.
(b) Factor: 3x²−5xy+2y² = (3x−2y)(x−y) = 0
Lines: 3x−2y=0 and x−y=0
Find area of a triangle having vertices A(1,2), B(4,6) and C(5,2).
Show model answer
Area = ½|1(6−2)+4(2−2)+5(2−6)| = ½|4+0−20|
= ½(16) = 8 sq units
Sessions with Introduction to Analytic Geometry questions
| Session | Questions |
|---|---|
| 2026 Annual | 5 |
| 2025 1st Annual | 6 |
| 2025 2nd Annual | 5 |
| 2024 Annual | 6 |
| 2023 Annual | 6 |
Common questions
What does the Introduction to Analytic Geometry chapter cover on this page?
28 real Federal Board (FBISE) Mathematics questions on Introduction to Analytic Geometry from 2023 to 2026, for 12th class. Each one shows the session it came from.
Are the answers official?
No. We could not find an official FBISE marking scheme for these papers, so the answers and explanations are written by Tayyari Karo for practice. Check anything important with your teacher or textbook.
Is it free?
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