Advertisements
Advertisements
Question
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
Solution
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
RELATED QUESTIONS
On which axis do the following points lie?
Q(0, -2)
Find the coordinates of the point where the diagonals of the parallelogram formed by joining the points (-2, -1), (1, 0), (4, 3) and(1, 2) meet
Three consecutive vertices of a parallelogram are (-2,-1), (1, 0) and (4, 3). Find the fourth vertex.
In what ratio is the line segment joining the points (-2,-3) and (3, 7) divided by the y-axis? Also, find the coordinates of the point of division.
Prove that the points A(-4,-1), B(-2, 4), C(4, 0) and D(2, 3) are the vertices of a rectangle.
The line segment joining the points P(3, 3) and Q(6, -6) is trisected at the points A and B such that Ais nearer to P. If A also lies on the line given by 2x + y + k = 0, find the value of k.
Show that the points A (1, 0), B (5, 3), C (2, 7) and D (−2, 4) are the vertices of a parallelogram.
In what ratio does the point P(2,5) divide the join of A (8,2) and B(-6, 9)?
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.
In what ratio does the point C (4,5) divides the join of A (2,3) and B (7,8) ?
The abscissa and ordinate of the origin are
Points (−4, 0) and (7, 0) lie
Write the coordinates of the point dividing line segment joining points (2, 3) and (3, 4) internally in the ratio 1 : 5.
If the mid-point of the segment joining A (x, y + 1) and B (x + 1, y + 2) is C \[\left( \frac{3}{2}, \frac{5}{2} \right)\] , find x, y.
If Points (1, 2) (−5, 6) and (a, −2) are collinear, then a =
The distance of the point (4, 7) from the y-axis is
In which quadrant does the point (-4, -3) lie?
Find the coordinates of point A, where AB is a diameter of the circle with centre (–2, 2) and B is the point with coordinates (3, 4).
If the perpendicular distance of a point P from the x-axis is 5 units and the foot of the perpendicular lies on the negative direction of x-axis, then the point P has ______.
The distance of the point (–4, 3) from y-axis is ______.
