Q3 of 35 Page 787

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

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


Formula:


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


D=


Here,


(x1,y1,z1)= (4, 6, -3)


(x2,y2,z2)= (0, 2, 3)


(x3,y3,z3)= (-4, -4, -1)


Length AB =


=


=


=


= = 2


Length BC =


=


=


=


= = 2


Length AC =


=


=


=


=


Here, AB = BC


∴ vertices A, B, C forms an isosceles triangle.


More from this chapter

All 35 →
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


 2

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

 5

Show that the points A(1, 1, 1), B(-2, 4, 1), C(1, -5, 5) and D(2, 2, 5) are the vertices of a square.