Advertisements
Advertisements
Question
Show that the following points taken in order to form an equilateral triangle
`"A"(sqrt(3), 2), "B"(0, 1), "C"(0, 3)`
Advertisements
Solution
Distance = `sqrt((x_2 - x_1)^2 + (y_2 - y_1)^2`
AB = `sqrt((0 - sqrt(3))^2 + (1 - 2)^2`
= `sqrt((- sqrt(3))^2 + (-1)^2`
= `sqrt(3 + 1)`
= `sqrt(4)`
= 2
BC = `sqrt((0 - 0)^2 + (3 - 1)^2`
= `sqrt(0^2 + 2^2)`
= `sqrt(4)`
= 2
AC = `sqrt((0 - sqrt(3))^2 + (3 - 2)^2`
= `sqrt((- sqrt(3))^2 + 1^2)`
= `sqrt(3 + 1)`
= `sqrt(4)`
= 2
AB = BC = AC ...(Three sides are equal)
∴ ABC is an equilateral triangle.
APPEARS IN
RELATED QUESTIONS
If the co-ordinate of A is x and that of B is y, find d(A, B).
x = -3, y = -6
Find d(A, B), if co-ordinates of A and B are -2 and 5 respectively.
Co-ordinates of the pair of points are given below. Hence find the distance between the pair.
-9, -1
Co-ordinates of the pair of points are given below. Hence find the distance between the pair.
x + 3, x - 3
Determine whether the given set of points are collinear or not
(a, −2), (a, 3), (a, 0)
Show that the following points taken in order to form the vertices of a parallelogram
A(−3, 1), B(−6, −7), C(3, −9) and D(6, −1)
The radius of a circle with centre at origin is 30 units. Write the coordinates of the points where the circle intersects the axes. Find the distance between any two such points.
Find the distance with the help of the number line given below.
d(J, H)
Find the distance with the help of the number line given below.
d(K, O)
Find the distance with the help of the number line given below.
d(P, J)
