Advertisements
Advertisements
प्रश्न
Find the value of k, if the point P (0, 2) is equidistant from (3, k) and (k, 5).
उत्तर
The distance d between two points `(x_1,y_1)` and `(x_2, y_2)` is given by the formula
`d = sqrt((x_1 - x_2)^2 + (y_1 - y_2)^2)`
It is said that P(0,2) is equidistant from both A(3,k) and B(k,5).
So, using the distance formula for both these pairs of points we have
`AP =sqrt((3)^2 + (k - 2)^2)`
`BP = sqrt((k)^2 + (3)^2)`
Now since both these distances are given to be the same, let us equate both.
AP = Bp
`sqrt((3)^2 + (k -2)^2) = sqrt((k)^2 + (3)^2)`
Squaring on both sides we have,
`(3)^2 + (k - 2)^2 = (k)^2 + (3)^2`
`9 + k^2 + 4 - 4k = k^2 + 9`
4k = 4
k = 1
Hence the value of ‘k’ for which the point ‘P’ is equidistant from the other two given points is k = 1
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
Find the coordinates of the circumcentre of the triangle whose vertices are (3, 0), (-1, -6) and (4, -1). Also, find its circumradius.
If three consecutive vertices of a parallelogram are (1, -2), (3, 6) and (5, 10), find its fourth vertex.
If A and B are (1, 4) and (5, 2) respectively, find the coordinates of P when AP/BP = 3/4.
Determine the ratio in which the point P (m, 6) divides the join of A(-4, 3) and B(2, 8). Also, find the value of m.
Find the co-ordinates of the point equidistant from three given points A(5,3), B(5, -5) and C(1,- 5).
If the point P (2,2) is equidistant from the points A ( -2,K ) and B( -2K , -3) , find k. Also, find the length of AP.
Show that the following points are the vertices of a square:
A (0,-2), B(3,1), C(0,4) and D(-3,1)
If the point C(k,4) divides the join of A(2,6) and B(5,1) in the ratio 2:3 then find the value of k.
Find the coordinates of the circumcentre of a triangle whose vertices are (–3, 1), (0, –2) and (1, 3).
If A(−3, 5), B(−2, −7), C(1, −8) and D(6, 3) are the vertices of a quadrilateral ABCD, find its area.
If R (x, y) is a point on the line segment joining the points P (a, b) and Q (b, a), then prove that x + y = a + b.
If x is a positive integer such that the distance between points P (x, 2) and Q (3, −6) is 10 units, then x =
The distance between the points (a cos θ + b sin θ, 0) and (0, a sin θ − b cos θ) is
If three points (0, 0), \[\left( 3, \sqrt{3} \right)\] and (3, λ) form an equilateral triangle, then λ =
If the area of the triangle formed by the points (x, 2x), (−2, 6) and (3, 1) is 5 square units , then x =
The ratio in which the line segment joining P (x1, y1) and Q (x2, y2) is divided by x-axis is
A line intersects the y-axis and x-axis at P and Q , respectively. If (2,-5) is the mid-point of PQ, then the coordinates of P and Q are, respectively
Write the X-coordinate and Y-coordinate of point P(– 5, 4)
Find the coordinates of the point whose abscissa is 5 and which lies on x-axis.
