Question

In the given figure, Δ ABC is an equilateral triangle. AD is a median of the triangle joining the points `A(0, (5sqrt3)/2), D(0, 0)`. Points B and C are (in same order):

विकल्प

• (−5, 0), (5, 0)

• `((−5)/2, 0), (5/2, 0)`

• (−10, 0), (10, 0)

• `(−5sqrt3, 0), (5sqrt3, 0)`

Answer 1

`((−5)/2, 0), (5/2, 0)`

Explanation:

Given: A = `(0, (5sqrt3)/2)`

D = (0, 0)

In an equilateral triangle, the median is also the altitude. Since A and D lie on the y-axis, the base BC must lie on the x-axis.

Length of altitude AD = `sqrt((0 - 0)^2 + ((5sqrt3)/2 - 0)^2)`

= `sqrt(0 + ((5sqrt3)/2)^2)`

= `(5sqrt3)/2`

For an equilateral triangle with side a, altitude h = `sqrt3/2 a`

`(5sqrt3)/2 = sqrt3/2 a`

Since D(0,0) is the midpoint of BC and the side length is 5 units:

BD = DC = `5/2`

Coordinates of B (to the left of the origin): `((−5)/2, 0)`

Coordinates of C (to the right of origin): `(5/2, 0)`