Advertisements
Advertisements
प्रश्न
The distance between the points (a cos θ + b sin θ, 0) and (0, a sin θ − b cos θ) is
पर्याय
a2 + b2
a + b
a2 − b2
- \[\sqrt{a2 + b2}\]
उत्तर
We have to find the distance betweenA` (a cos theta + b sin theta , 0 ) " and " B(0, a sin theta - b cos theta )` .
In general, the distance between A(x1 , y 1) and B(x2 , y2) is given by,
`AB = sqrt((x_2 - x_1 )^2 + (y_2 - y_1 )^2)`
So,
`AB = sqrt((a cos theta + b sin theta - 0)^2 + (0- a sin theta + b cos theta
)^2)`
`= sqrt((a^2 (sin^2 theta + cos^2 theta ) + b^2 (sin^2 theta + cos^2 theta)`
But according to the trigonometric identity,
`sin^2 theta + cos^2 theta = 1`
Therefore,
`AB = sqrt(a^2 + b^2)`
APPEARS IN
संबंधित प्रश्न
(Street Plan): A city has two main roads which cross each other at the centre of the city. These two roads are along the North-South direction and East-West direction.
All the other streets of the city run parallel to these roads and are 200 m apart. There are 5 streets in each direction. Using 1cm = 200 m, draw a model of the city on your notebook. Represent the roads/streets by single lines.
There are many cross- streets in your model. A particular cross-street is made by two streets, one running in the North - South direction and another in the East - West direction. Each cross street is referred to in the following manner : If the 2nd street running in the North - South direction and 5th in the East - West direction meet at some crossing, then we will call this cross-street (2, 5). Using this convention, find:
- how many cross - streets can be referred to as (4, 3).
- how many cross - streets can be referred to as (3, 4).
The three vertices of a parallelogram are (3, 4) (3, 8) and (9, 8). Find the fourth vertex.
In the seating arrangement of desks in a classroom three students Rohini, Sandhya and Bina are seated at A(3, 1), B(6, 4), and C(8, 6). Do you think they are seated in a line?
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.
Show that the points A(2,1), B(5,2), C(6,4) and D(3,3) are the angular points of a parallelogram. Is this figure a rectangle?
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.
Show that the following points are the vertices of a rectangle
A (0,-4), B(6,2), C(3,5) and D(-3,-1)
Find the area of quadrilateral PQRS whose vertices are P(-5, -3), Q(-4,-6),R(2, -3) and S(1,2).
Find the coordinates of the centre of the circle passing through the points P(6, –6), Q(3, –7) and R (3, 3).
Find the possible pairs of coordinates of the fourth vertex D of the parallelogram, if three of its vertices are A(5, 6), B(1, –2) and C(3, –2).
ΔXYZ ∼ ΔPYR; In ΔXYZ, ∠Y = 60o, XY = 4.5 cm, YZ = 5.1 cm and XYPY =` 4/7` Construct ΔXYZ and ΔPYR.
A point whose abscissa and ordinate are 2 and −5 respectively, lies in
ABCD is a parallelogram with vertices \[A ( x_1 , y_1 ), B \left( x_2 , y_2 \right), C ( x_3 , y_3 )\] . Find the coordinates of the fourth vertex D in terms of \[x_1 , x_2 , x_3 , y_1 , y_2 \text{ and } y_3\]
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 three points (x1, y1) (x2, y2), (x3, y3) lie on the same line, prove that \[\frac{y_2 - y_3}{x_2 x_3} + \frac{y_3 - y_1}{x_3 x_1} + \frac{y_1 - y_2}{x_1 x_2} = 0\]
Write the ratio in which the line segment joining points (2, 3) and (3, −2) is divided by X axis.
If P (x, 6) is the mid-point of the line segment joining A (6, 5) and B (4, y), find y.
Find the area of triangle with vertices ( a, b+c) , (b, c+a) and (c, a+b).
The point R divides the line segment AB, where A(−4, 0) and B(0, 6) such that AR=34AB.">AR = `3/4`AB. Find the coordinates of R.
The distance of the point (–4, 3) from y-axis is ______.
