Home
Class 12
MATHS
A traingle has its three sides equal to ...

A traingle has its three sides equal to a,b and c . If the co-ordinates of its vertices are `A(x_(1),y_(1))`, `B(x_(2),y_(2))` and `C(x_(3),y_(3))`, show that :
`|{:(x_(1),y_(1),2),(x_(2),y_(2),2),(x_(3),y_(3),2):}|^(2)=(a+b+c)(b+c-a)(c+a-b)(a+b-c)`.

Promotional Banner

Topper's Solved these Questions

  • DETERMINANTS

    MODERN PUBLICATION|Exercise FREQUENTLY ASKED QUESTIONS|17 Videos

  • DETERMINANTS

    MODERN PUBLICATION|Exercise Examples (FREQUENCY ASKED QUESTIONS)|28 Videos

  • CONTINUITY AND DIFFERENTIABILITY

    MODERN PUBLICATION|Exercise CHAPTER TEST|12 Videos

  • DIFFERENTIAL EQUATIONS

    MODERN PUBLICATION|Exercise CHAPTER TEST (9)|12 Videos

Similar Questions

Explore conceptually related problems

A triangle has its three sides equal to a , b and c . If the coordinates of its vertices are A(x_1, y_1),B(x_2,y_2)a n dC(x_3,y_3), show that |[x_1,y_1, 2],[x_2,y_2, 2],[x_3,y_3, 2]|^2=(a+b+c)(b+c-a)(c+a-b)(a+b-c)

The centroid of the triangle with vertices at A(x_(1),y_(1)),B(x_(2),y_(2)),c(x_(3),y_(3)) is

The centroid of the triangle formed by A(x_(1),y_(1)),B(x_(2),y_(2)),C(x_(3),y_(3)) is

The area of the Quadrilateral with vertices A(x_(1),y_(1)),B(x_(2),y_(2)),C(x_(3),y_(3)) and D(x_(4),y_(4)) is

The co-ordinates of incentre of the triangle whose vertices are given by A(x_(1), y_(1)), B(x_(2), y_(2)), C(x_(3), y_(3)) is

If (x_1-x_2)^2+(y_1-y_2)^2=a^2,(x_2-x_3)^2+(y_2-y_3)^2=b^2 and (x_3-x_1)^2+(y_3-y_1)^2=c^2 then prove that 4|{:(x_1,y_1,1),(x_2,y_2,1),(x_3,y_3,1):}|= (a+b+c)(b+c-a)(c+a-b)(a+b-c)

Prove that the coordinates of the centre of the circle inscribed in the triangle,whose vertices are the points (x_(1),y_(1)),(x_(2),y_(2)) and (x_(3),y_(3)) are (ax_(1)+bx_(2)+cx_(3))/(a+b+c) and (ay_(1)+by_(2)+cy_(3))/(a+b+c)

If A(x_(1),y_(1)),B(x_(2),y_(2)),C(x_(3),y_(3)) are the vertices of the triangle then show that:'

If A (x_(1), y_(1)), B (x_(2), y_(2)) and C (x_(3), y_(3)) are vertices of an equilateral triangle whose each side is equal to a, then prove that |(x_(1),y_(1),2),(x_(2),y_(2),2),(x_(3),y_(3),2)| is equal to

If A(3x_(1),3y_(1)),B(3x_(2),3y_(2)),C(3x_(3),3y_(3)) are vertices of a triangle with orthocentre H at (x_(1)+x_(2)+x_(3),y_(1)+y_(2)+y_(3)) then the /_ABC=