Advertisements
Advertisements
प्रश्न
The distance between the points (cos θ, 0) and (sin θ − cos θ) is
विकल्प
- \[\sqrt{3}\]
- \[\sqrt{2}\]
2
1
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
The three vertices of a parallelogram are (3, 4) (3, 8) and (9, 8). Find the fourth vertex.
Show that the points (−3, 2), (−5,−5), (2, −3) and (4, 4) are the vertices of a rhombus. Find the area of this rhombus.
The points (3, -4) and (-6, 2) are the extremities of a diagonal of a parallelogram. If the third vertex is (-1, -3). Find the coordinates of the fourth vertex.
If the points A (a, -11), B (5, b), C (2, 15) and D (1, 1) are the vertices of a parallelogram ABCD, find the values of a and b.
If the poin A(0,2) is equidistant form the points B (3, p) and C (p ,5) find the value of p. Also, find the length of AB.
If the point P (2,2) is equidistant from the points A ( -2,K ) and B( -2K , -3) , find k. Also, find the length of AP.
Show hat A(1,2), B(4,3),C(6,6) and D(3,5) are the vertices of a parallelogram. Show that ABCD is not rectangle.
Find the ratio in which the pint (-3, k) divide the join of A(-5, -4) and B(-2, 3),Also, find the value of k.
If the point A(0,2) is equidistant from the points B(3,p) and C(p, 5), find p.
Find the coordinates of the circumcentre of a triangle whose vertices are (–3, 1), (0, –2) and (1, 3).
Mark the correct alternative in each of the following:
The point of intersect of the coordinate axes is
The distance of the point P (4, 3) from the origin is
The points \[A \left( x_1 , y_1 \right) , B\left( x_2 , y_2 \right) , C\left( x_3 , y_3 \right)\] are the vertices of ΔABC .
(i) The median from A meets BC at D . Find the coordinates of the point D.
(ii) Find the coordinates of the point P on AD such that AP : PD = 2 : 1.
(iii) Find the points of coordinates Q and R on medians BE and CF respectively such thatBQ : QE = 2 : 1 and CR : RF = 2 : 1.
(iv) What are the coordinates of the centropid of the triangle ABC ?
If A (2, 2), B (−4, −4) and C (5, −8) are the vertices of a triangle, than the length of the median through vertex C is
If (−1, 2), (2, −1) and (3, 1) are any three vertices of a parallelogram, then
If points (t, 2t), (−2, 6) and (3, 1) are collinear, then t =
The ratio in which (4, 5) divides the join of (2, 3) and (7, 8) is
The length of a line segment joining A (2, −3) and B is 10 units. If the abscissa of B is 10 units, then its ordinates can be
Write the X-coordinate and Y-coordinate of point P(– 5, 4)
Assertion (A): Mid-point of a line segment divides the line segment in the ratio 1 : 1
Reason (R): The ratio in which the point (−3, k) divides the line segment joining the points (− 5, 4) and (− 2, 3) is 1 : 2.
