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
If the points A(k + 1, 2k), B(3k, 2k + 3) and C(5k − 1, 5k) are collinear, then find the value of k
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.
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.
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.
In what ratio does the point (−4, 6) divide the line segment joining the points A(−6, 10) and B(3,−8)?
If (2, p) is the midpoint of the line segment joining the points A(6, -5) and B(-2,11) find the value of p.
If the points P (a,-11) , Q (5,b) ,R (2,15) and S (1,1). are the vertices of a parallelogram PQRS, find the values of a and b.
Find the ratio in which the line segment joining the points A(3, −3) and B(−2, 7) is divided by the x-axis. Also, find the coordinates of the point of division.
Find the centroid of the triangle whose vertices is (−2, 3) (2, −1) (4, 0) .
If the point P (m, 3) lies on the line segment joining the points \[A\left( - \frac{2}{5}, 6 \right)\] and B (2, 8), find the value of m.
Find the value(s) of k for which the points (3k − 1, k − 2), (k, k − 7) and (k − 1, −k − 2) are collinear.
If the distance between points (x, 0) and (0, 3) is 5, what are the values of x?
If the centroid of the triangle formed by the points (a, b), (b, c) and (c, a) is at the origin, then a3 + b3 + c3 =
If points A (5, p) B (1, 5), C (2, 1) and D (6, 2) form a square ABCD, then p =
The coordinates of the fourth vertex of the rectangle formed by the points (0, 0), (2, 0), (0, 3) are
The coordinates of the point P dividing the line segment joining the points A (1, 3) and B(4, 6) in the ratio 2 : 1 are
If A(x, 2), B(−3, −4) and C(7, −5) are collinear, then the value of x is
Point (0, –7) lies ______.
If the points P(1, 2), Q(0, 0) and R(x, y) are collinear, then find the relation between x and y.
Given points are P(1, 2), Q(0, 0) and R(x, y).
The given points are collinear, so the area of the triangle formed by them is `square`.
∴ `1/2 |x_1(y_2 - y_3) + x_2(y_3 - y_1) + x_3(y_1 - y_2)| = square`
`1/2 |1(square) + 0(square) + x(square)| = square`
`square + square + square` = 0
`square + square` = 0
`square = square`
Hence, the relation between x and y is `square`.
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.
