Q8 of 53 Page 107

Show that the points A(1, 2), B(1, 6), C(1 + 2 √3, 4) are vertices of an equilateral triangle.

For an equilateral triangle, all its sides are equal.

According to the distance formula, the distance 'd' between two points (a,b) and (c,d) is given by
 .....(1)


Length AB = = = 4


Length BC = = = 4


Length AC = = = 4


Hence The given points form an equilateral triangle.


More from this chapter

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6

Show that points A(-4, -7), B(-1, 2), C(8, 5) and D(5, -4) are vertices of a rhombus ABCD.

 7

Find x if distance between points L(x, 7) and M(1, 15) is 10.

 1

Find the coordinates of point P if P divides the line segment joining the points A(-1,7) and B(4,-3) in the ratio 2:3.

 2

In each of the following examples find the co-ordinates of point A which divides segment PQ in the ratio a:b.

(1) P(-3, 7), Q(1, -4), a:b = 2:1


(2) P(-2, -5), Q(4, 3), a:b = 3:4


(3) P(2, 6), Q(-4, 1), a:b = 1:2