TS EAMCET · Maths · Three Dimensional Geometry

Assertion $(A)$ : If $(- 1, 3, 2)$ and $(5, 3, 2)$ are respectively the orthocentre and circumcentre of a triangle, then $(3, 3, 2)$ is its centroid. Reason $(R)$ : Centroid of the triangle divides the line segment joining the orthocentre and the circumcentre in the ratio $1 : 2$ . Which one of the following is true?

A $(A)$ and $(R)$ are true and $(R)$ is the correct explanation to $(A)$
B $(A)$ and $(R)$ are true but $(R)$ is not the correct explanation to $(A)$
C $(A)$ is true, $(R)$ is false
D $(A)$ is false, $(R)$ is true

Verified Solution

Answer & Solution

Correct Answer

(C) $(A)$ is true, $(R)$ is false

Step-by-step Solution

Detailed explanation

(A): Orthocentre is A-1,3,2 Circumcentre is B5,3,2 Centroid is C3,3,2 The point C divides the line joining of AB in the ratio 2:1 internally, then Centroid =25+1-12+1,23+132+1,22+122+1 =10-13,6+33,4+23 =3,3,2 ∴ A is true and R is false.

Apply the relevant identity from the chapter and substitute the values established in the previous step, keeping the original constraint in view.

Use the simplified expression to isolate the unknown, then plug the result back into the question setup to confirm the working is internally consistent.

Cross-check against a boundary or limiting case. Both the dimensional balance and the qualitative behaviour at the extreme should agree with the candidate answer.

Combine the steps above to identify the correct option. The remaining choices each fail at least one of the consistency, dimensional, or boundary checks.

Same subject

Explore more questions on app

From TS EAMCET

Explore more questions on app

$X = x$	$0$	$1$	$2$	$3$	4	$5$	$6$	$7$
$P (x)$	$0.01$	$0.10$	$0.26$	$0.33$	$0.18$	$0.06$	$K$	$0.04$

Assertion A: If -1,3,2 and 5,3,2 are respectively the orthocentre and circumcentre of a triangle, then 3,3,2 is its centroid. Reason R: Centroid of the triangle divides the line segment joining the orthocentre and the circumcentre in the ratio 1:2. Which one of the following is true?

Step-by-step Solution