Q2 of 35 Page 787

Show that the points A(1, -1, -5), b(3, 1,3) and C(9, 1, -3) are the vertices of an equilateral triangle.

To prove: Points A, B, C form equilateral triangle.


Formula:


The distance between two points (x1,y1,z1) and (x2,y2,z2) is given by


D=


Here,


(x1,y1,z1)= (1, -1, -5)


(x2,y2,z2)= (3, 1,3)


(x3,y3,z3)= (9, 1, -3)


Length AB =


=


=


=


= = 6


Length BC =


=


=


=


= = 6


Length AC =


=


=


=


= = 6


Hence, AB = BC = AC


Therefore, Points A, B, C make an equilateral triangle.


More from this chapter

All 35 →
4

In which octant does each of the given points lie?

(i) (-4, -1, -6)


(ii) (2, 3, -4)


(iii) (-6, 5, -1)


(iv) (4, -3, -2)


(v) (-1, -6, 5)


(vi) (4, 6, 8)


 1

Find the distance between the points :

(i) A(5, 1, 2) and B(4, 6, -1)


(ii) P(1, -1, 3) and Q(2, 3, -5)


(iii) R(1, -3, 4) and S(4, -2, -3)


(iv) C(9, -12, -8) and the origin


 3

Show that the points A(4, 6, -5), B(0, 2, 3) and C(-4, -4, -1) from the vertices of an isosceles triangle.

 4

Show that the points A(0, 1, 2), B(2, -1, 3) and C(1, -3, 1) are the vertices of an isosceles right-angled triangle.