Class CBSE Class 12 Mathematics Three Dimensional Geometry Q #1729
COMPETENCY BASED
APPLY
1 Marks 2026 AISSCE(Board Exam) MCQ SINGLE
If points $(2, 3)$, $(0, 4)$ and $(p, 2)$ are collinear, then the value of p is:
(A) $\frac{4}{7}$
(B) $-\frac{3}{7}$
(C) 4
(D) -4
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Correct Answer: C

AI Tutor Explanation

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Detailed Solution

Step 1: Understand the Condition for Collinearity

Three points are collinear if the area of the triangle formed by them is zero. Alternatively, the slope of the line segment joining the first two points must be equal to the slope of the line segment joining the second and third points.

Step 2: Calculate Slopes

Let the points be $A(2, 3)$, $B(0, 4)$, and $C(p, 2)$. The slope $m_{AB}$ is: $$m_{AB} = \frac{4 - 3}{0 - 2} = \frac{1}{-2} = -0.5$$ The slope $m_{BC}$ is: $$m_{BC} = \frac{2 - 4}{p - 0} = \frac{-2}{p}$$

Step 3: Equate Slopes and Solve for p

Since the points are collinear, $m_{AB} = m_{BC}$: $$\frac{1}{-2} = \frac{-2}{p}$$ Cross-multiplying gives: $$p = (-2) \times (-2) = 4$$

Final Answer: 4

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Pedagogical Audit
Bloom's Analysis: This is an APPLY question because the student must utilize the geometric property of collinearity (slope equality) to solve for an unknown variable.
Knowledge Dimension: PROCEDURAL
Justification: The question requires the application of a specific mathematical algorithm (slope formula) to reach a solution.
Syllabus Audit: In the context of CBSE Class 12, this is classified as COMPETENCY. This tests the student's ability to bridge coordinate geometry concepts with algebraic manipulation.

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