Advertisements
Advertisements
प्रश्न
Find the distances between the following point.
A(a, 0), B(0, a)
Advertisements
उत्तर
A(a, 0), B(0, a)
\[AB = \sqrt{\left( 0 - a \right)^2 + \left( a - 0 \right)^2}\]
\[ = \sqrt{a^2 + a^2}\]
\[ = \sqrt{2 a^2}\]
\[ = a\sqrt{2}\]
APPEARS IN
संबंधित प्रश्न
The x-coordinate of a point P is twice its y-coordinate. If P is equidistant from Q(2, –5) and R(–3, 6), find the coordinates of P.
Show that the points (a, a), (–a, –a) and (– √3 a, √3 a) are the vertices of an equilateral triangle. Also find its area.
If P and Q are two points whose coordinates are (at2 ,2at) and (a/t2 , 2a/t) respectively and S is the point (a, 0). Show that `\frac{1}{SP}+\frac{1}{SQ}` is independent of t.
If the distances of P(x, y) from A(5, 1) and B(–1, 5) are equal, then prove that 3x = 2y
Prove that the points A(1, 7), B (4, 2), C(−1, −1) D (−4, 4) are the vertices of a square.
Find the distance between the points
A(1,-3) and B(4,-6)
Distance of point (−3, 4) from the origin is ______.
Find the distance between the following pair of point in the coordinate plane.
(1 , 3) and (3 , 9)
Find the relation between x and y if the point M (x,y) is equidistant from R (0,9) and T (14 , 11).
x (1,2),Y (3, -4) and z (5,-6) are the vertices of a triangle . Find the circumcentre and the circumradius of the triangle.
Find the co-ordinates of points on the x-axis which are at a distance of 17 units from the point (11, -8).
A point P (2, -1) is equidistant from the points (a, 7) and (-3, a). Find a.
Prove that the points A (1, -3), B (-3, 0) and C (4, 1) are the vertices of an isosceles right-angled triangle. Find the area of the triangle.
Given A = (3, 1) and B = (0, y - 1). Find y if AB = 5.
Give the relation that must exist between x and y so that (x, y) is equidistant from (6, -1) and (2, 3).
Show that the points (a, a), (-a, -a) and `(-asqrt(3), asqrt(3))` are the vertices of an equilateral triangle.
Show that the point (11, –2) is equidistant from (4, –3) and (6, 3).
The distance of the point P(–6, 8) from the origin is ______.
|
Case Study Trigonometry in the form of triangulation forms the basis of navigation, whether it is by land, sea or air. GPS a radio navigation system helps to locate our position on earth with the help of satellites. |
- Make a labelled figure on the basis of the given information and calculate the distance of the boat from the foot of the observation tower.
- After 10 minutes, the guard observed that the boat was approaching the tower and its distance from tower is reduced by 240(`sqrt(3)` - 1) m. He immediately raised the alarm. What was the new angle of depression of the boat from the top of the observation tower?

