Advertisements
Advertisements
प्रश्न
The base PQ of two equilateral triangles PQR and PQR' with side 2a lies along y-axis such that the mid-point of PQ is at the origin. Find the coordinates of the vertices R and R' of the triangles.
Advertisements
उत्तर
In an equilateral triangle, the height ‘h’ is given by
`h =(sqrt3`("Side of the equilateral triangle"))/2`
Here it is given that 'PQ' forms the base of two equilateral triangles whose side measures '2a' units.
The height of these two equilateral triangles has got to be
`h = (sqrt3("Side of the equilateral triangle"))/2`
`= (sqrt3(2a))/2`
`h = asqrt3`
In an equilateral triangle, the height drawn from one vertex meets the midpoint of the side opposite this vertex.
So here we have ‘PQ’ being the base lying along the y-axis with its midpoint at the origin, that is at (0, 0)
So the vertices ‘R’ and ‘R’’ will lie perpendicularly to the y-axis on either side of the origin at a distance of `asqrt3` units
Hence the co-ordinates of ‘R’ and ‘R’’ are
`R(asqrt3,0)`
`R'(-a sqrt3, 0)`
APPEARS IN
संबंधित प्रश्न
Let ABCD be a square of side 2a. Find the coordinates of the vertices of this square when A coincides with the origin and AB and AD are along OX and OY respectively.
Find the distance between the following pair of points:
(a, 0) and (0, b)
Find the points of trisection of the line segment joining the points:
(2, -2) and (-7, 4).
Show that the following points are the vertices of a square:
A (6,2), B(2,1), C(1,5) and D(5,6)
Show that the following points are the vertices of a rectangle
A (0,-4), B(6,2), C(3,5) and D(-3,-1)
Find the ratio in which the point (-1, y) lying on the line segment joining points A(-3, 10) and (6, -8) divides it. Also, find the value of y.
If the point A(0,2) is equidistant from the points B(3,p) and C(p, 5), find p.
If the points A(4,3) and B( x,5) lie on the circle with center O(2,3 ) find the value of x .
The abscissa of a point is positive in the
Find the centroid of the triangle whose vertices is (−2, 3) (2, −1) (4, 0) .
If the vertices of a triangle are (1, −3), (4, p) and (−9, 7) and its area is 15 sq. units, find the value(s) of p.
If the points A(−2, 1), B(a, b) and C(4, −1) ae collinear and a − b = 1, find the values of aand b.
The perimeter of the triangle formed by the points (0, 0), (0, 1) and (0, 1) is
If A (5, 3), B (11, −5) and P (12, y) are the vertices of a right triangle right angled at P, then y=
If the points(x, 4) lies on a circle whose centre is at the origin and radius is 5, then x =
The coordinates of a point on x-axis which lies on the perpendicular bisector of the line segment joining the points (7, 6) and (−3, 4) are
If the coordinates of the two points are P(–2, 3) and Q(–3, 5), then (abscissa of P) – (abscissa of Q) is ______.
(–1, 7) is a point in the II quadrant.
Co-ordinates of origin are ______.
The distance of the point (–6, 8) from x-axis is ______.
