Advertisements
Advertisements
प्रश्न
Write the distance between the points A (10 cos θ, 0) and B (0, 10 sin θ).
Advertisements
उत्तर
We have to find the distance between A( 10 cos θ,0) and B(0 , 10 sin θ ) .
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((10 cos θ - 0)^2 + (0 - 10 sin θ)^2)`
` = sqrt(10^2 (sin^2 θ + cos^2 θ ) `
But according to the trigonometric identity,
`sin^2 θ + cos^2 θ = 1`
Therefore,
AB = 10
APPEARS IN
संबंधित प्रश्न
Let ABCD be a square of side 2a. Find the coordinates of the vertices of this square when A coincides with the origin and AB and AD are along OX and OY respectively.
The three vertices of a parallelogram are (3, 4) (3, 8) and (9, 8). Find the fourth vertex.
Prove that the points (4, 5) (7, 6), (6, 3) (3, 2) are the vertices of a parallelogram. Is it a rectangle.
Show that the following points are the vertices of a square:
A (6,2), B(2,1), C(1,5) and D(5,6)
Show that the following points are the vertices of a rectangle.
A (2, -2), B(14,10), C(11,13) and D(-1,1)
Find the coordinates of the midpoints of the line segment joining
P(-11,-8) and Q(8,-2)
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.
Find the area of quadrilateral ABCD whose vertices are A(-3, -1), B(-2,-4) C(4,-1) and D(3,4)
If the vertices of ΔABC be A(1, -3) B(4, p) and C(-9, 7) and its area is 15 square units, find the values of p
Show that `square` ABCD formed by the vertices A(-4,-7), B(-1,2), C(8,5) and D(5,-4) is a rhombus.
In \[∆\] ABC , the coordinates of vertex A are (0, - 1) and D (1,0) and E(0,10) respectively the mid-points of the sides AB and AC . If F is the mid-points of the side BC , find the area of \[∆\] DEF.
Find the value of k, if the points A(7, −2), B (5, 1) and C (3, 2k) are collinear.
Write the ratio in which the line segment doining the points A (3, −6), and B (5, 3) is divided by X-axis.
The distance between the points (a cos θ + b sin θ, 0) and (0, a sin θ − b cos θ) is
If A (5, 3), B (11, −5) and P (12, y) are the vertices of a right triangle right angled at P, then y=
If (x , 2), (−3, −4) and (7, −5) are collinear, then x =
The coordinates of a point on x-axis which lies on the perpendicular bisector of the line segment joining the points (7, 6) and (−3, 4) are
In Fig. 14.46, the area of ΔABC (in square units) is
Points (1, –1) and (–1, 1) lie in the same quadrant.
The coordinates of a point whose ordinate is `-1/2` and abscissa is 1 are `-1/2, 1`.
