Advertisements
Advertisements
प्रश्न
If three points (0, 0), \[\left( 3, \sqrt{3} \right)\] and (3, λ) form an equilateral triangle, then λ =
पर्याय
2
-3
-4
None of these
Advertisements
उत्तर
We have an equilateral triangle ΔABC whose co-ordinates are A (0, 0); B ` ( 3 ,sqrt(3))" and " C (3 , λ )` .
Since the triangle is equilateral. So,
`AB^2 = Ac^2`
So,
`(3 - 0)^2 + (sqrt(3) - 0)^2 = (3 - 0)^2 + (lambda - 0)^2`
Cancel out the common terms from both the sides,
Therefore,
`lambda = sqrt(3)`
APPEARS IN
संबंधित प्रश्न
Let ABCD be a square of side 2a. Find the coordinates of the vertices of this square when The centre of the square is at the origin and coordinate axes are parallel to the sides AB and AD respectively.
Find the value of k, if the point P (0, 2) is equidistant from (3, k) and (k, 5).
Name the quadrilateral formed, if any, by the following points, and given reasons for your answers:
A(4, 5) B(7, 6), C (4, 3), D(1, 2)
Prove that the points (3, -2), (4, 0), (6, -3) and (5, -5) are the vertices of a parallelogram.
Prove that the points (4, 5) (7, 6), (6, 3) (3, 2) are the vertices of a parallelogram. Is it 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.
In what ratio is the line segment joining A(2, -3) and B(5, 6) divide by the x-axis? Also, find the coordinates of the pint of division.
If the points A(−1, −4), B(b, c) and C(5, −1) are collinear and 2b + c = 4, find the values of b and c.
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.
Write the coordinates the reflections of points (3, 5) in X and Y -axes.
If the points P (x, y) is equidistant from A (5, 1) and B (−1, 5), then
If A(x, 2), B(−3, −4) and C(7, −5) are collinear, then the value of x is
What is the nature of the line which includes the points (-5, 5), (6, 5), (-3, 5), (0, 5)?
If segment AB is parallel Y-axis and coordinates of A are (1, 3), then the coordinates of B are ______
Point P(– 4, 2) lies on the line segment joining the points A(– 4, 6) and B(– 4, – 6).
Signs of the abscissa and ordinate of a point in the second quadrant are respectively.
The points whose abscissa and ordinate have different signs will lie in ______.
Point (3, 0) lies in the first quadrant.
The coordinates of the point where the line 2y = 4x + 5 crosses x-axis is ______.
Distance of the point (6, 5) from the y-axis is ______.
