JEE MATHEMATICS MCQ: 2D GEOMETRY SYSTEM

1 Easy

1 of 1

Analyzing +4 | -1

Let

k

be an integer such that the triangle with vertices

(k,-3 k),(5, k)

and

(-k, 2)

has area 28 sq units. Then, the orthocentre of this triangle is at the point

View answer and explanation

Correct option: A

\left(2, \frac{1}{2}\right)

Option A

\left(2, \frac{{1}}{{2}}\right)

is correct because after finding the value of k and the vertices, the orthocenter is calculated using properties of circumcenter and centroid.

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\alpha

(\alpha, 2 \alpha)

\Delta A B C

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

C(4,4)

P

2 P A=3 P B

A

(0,0)

B

(4,-3)

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

(2,0)

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

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

=0

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

(0,0)(3,0)

(0,4)