JEE MATHEMATICS MCQ: 2D GEOMETRY SYSTEM

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Analyzing +4 | -1

\triangle A B C

, base

B C

and area of triangle '

\triangle

' are fixed. Locus of the centroid of

\triangle A B C

is a straight line that is

View answer and explanation

Correct option: A

parallel to side

B C

Option A (parallel to side

BC

) is correct because with a fixed base and area, the height of the triangle is constant, implying the locus of the centroid is a line parallel to the base.

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Values of

\alpha

(\alpha, 2 \alpha)

lies inside the

\Delta A B C

A(0,2), B(2,0)

and

C(4,4)

The locus of the moving point

P

, such that

2 P A=3 P B

where

A

(0,0)

and

B

(4,-3)

, is The incentre of the triangle with vertices

(1, \sqrt{3}),(0,0)

and

(2,0)

is The triangle with vertex

(1,5),(-3,1) \,\&\,(-2,1)

is The area of the quadrilateral with its vertices at the foci of the conics

9 x^2-16 y^2-18 x+32 y-23

=0

and

25 x^2+9 y^2-50 x-18 y+33=0

, is Orthocentre of the triangle whose vertices are

(0,0)(3,0)

and

(0,4)