Advertisements
Advertisements
Question
Find a point on the y-axis which is equidistant from the points (5, 2) and (-4, 3).
Advertisements
Solution
Let the co-ordinates of the required point on y-axis be P (0, y).
The given points are A (5, 2) and B (-4, 3).
Given, PA = PB
PA2 = PB2
(0 -5)2 + (y -2)2 = (0 + 4)2 + (y - 3)2
25 + y2 + 4 - 4y = 16 + y2 + 9 - 6y
2y = -4
y = -2
Thus, the required point is (0, -2).
APPEARS IN
RELATED QUESTIONS
Show that four points (0, – 1), (6, 7), (–2, 3) and (8, 3) are the vertices of a rectangle. Also, find its area
If a≠b≠0, prove that the points (a, a2), (b, b2) (0, 0) will not be collinear.
If A (-1, 3), B (1, -1) and C (5, 1) are the vertices of a triangle ABC, find the length of the median through A.
P and Q are two points lying on the x - axis and the y-axis respectively . Find the coordinates of P and Q if the difference between the abscissa of P and the ordinates of Q is 1 and PQ is 5 units.
Prove that the points (0,3) , (4,3) and `(2, 3+2sqrt 3)` are the vertices of an equilateral triangle.
Prove that the points (0 , 0) , (3 , 2) , (7 , 7) and (4 , 5) are the vertices of a parallelogram.
A(2, 5), B(-2, 4) and C(-2, 6) are the vertices of a triangle ABC. Prove that ABC is an isosceles triangle.
Find distance between points O(0, 0) and B(– 5, 12)
Name the type of triangle formed by the points A(–5, 6), B(–4, –2) and C(7, 5).
|
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?
