Advertisements
Advertisements
प्रश्न
The distance between the points (cos θ, 0) and (sin θ − cos θ) is
पर्याय
- \[\sqrt{3}\]
- \[\sqrt{2}\]
2
1
Advertisements
उत्तर
We have to find the distance between ` A (cos theta , sin theta ) and B ( sin theta , - cos theta ) `.
In general, the distance between A`(x_1 , y_1) ` and B `(x_2 , y_2)` is given by,
`AB = sqrt ((x_2 - x_1 )^2 + ( y_2-y_1)^2)`
So,
`AB = sqrt(( sin theta - cos theta )^2 + ( - cos theta - sin theta )^2)`
` = sqrt( 2 ( sin ^2 theta + cos^2 theta ) `
But according to the trigonometric identity,
`sin^2 theta + cos^2 theta = 1`
Therefore,
AB = `sqrt (2) `
APPEARS IN
संबंधित प्रश्न
Which point on the x-axis is equidistant from (5, 9) and (−4, 6)?
Find the value of k, if the point P (0, 2) is equidistant from (3, k) and (k, 5).
If (−2, 3), (4, −3) and (4, 5) are the mid-points of the sides of a triangle, find the coordinates of its centroid.
Prove that the points (3, 0), (4, 5), (-1, 4) and (-2, -1), taken in order, form a rhombus.
Also, find its area.
Find the points of trisection of the line segment joining the points:
5, −6 and (−7, 5),
Determine the ratio in which the straight line x - y - 2 = 0 divides the line segment
joining (3, -1) and (8, 9).
Prove that the points (4, 5) (7, 6), (6, 3) (3, 2) are the vertices of a parallelogram. Is it a rectangle.
`"Find the ratio in which the poin "p (3/4 , 5/12) " divides the line segment joining the points "A (1/2,3/2) and B (2,-5).`
Prove that the diagonals of a rectangle ABCD with vertices A(2,-1), B(5,-1) C(5,6) and D(2,6) are equal and bisect each other
Find the coordinates of the points of trisection of the line segment joining the points (3, –2) and (–3, –4) ?
Find the coordinates of the circumcentre of a triangle whose vertices are (–3, 1), (0, –2) and (1, 3).
The abscissa and ordinate of the origin are
If (0, −3) and (0, 3) are the two vertices of an equilateral triangle, find the coordinates of its third vertex.
Find the value of k, if the points A(7, −2), B (5, 1) and C (3, 2k) are collinear.
Find the area of a parallelogram ABCD if three of its vertices are A(2, 4), B(2 + \[\sqrt{3}\] , 5) and C(2, 6).
Write the ratio in which the line segment joining points (2, 3) and (3, −2) is divided by X axis.
The perimeter of the triangle formed by the points (0, 0), (0, 1) and (0, 1) is
If points (a, 0), (0, b) and (1, 1) are collinear, then \[\frac{1}{a} + \frac{1}{b} =\]
The distance of the point (4, 7) from the x-axis is
Statement A (Assertion): If the coordinates of the mid-points of the sides AB and AC of ∆ABC are D(3, 5) and E(–3, –3) respectively, then BC = 20 units.
Statement R (Reason): The line joining the mid-points of two sides of a triangle is parallel to the third side and equal to half of it.
