Advertisements
Advertisements
Question
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.
Advertisements
Solution
As per the question, we have
AP = BP
`⇒sqrt((2+2)^2 +(2+k)^2) = sqrt(( 2+2k)^2 +(2+3)^2)`
`⇒sqrt((4)^2 +(2-k)^2) = sqrt((2+2k)^2 + (5)^2)`
⇒ 16+ 4 +k2 - 4k = 4+ 4k2 + 8k +25 (Squaring both sides)
`⇒k^2 + 4k +3=0`
⇒ (k+1) (k+3) =0
⇒ k =-3, -1
Now for k = -1
`AP= sqrt ((2+2)^2 +(2-k)^2)`
`= sqrt((4)^2 +(2+1)^2)`
`= sqrt(16+9) = 5` units
For k = -3
`AP= sqrt(( 2+2)^2 +(2-k)^2)`
`= sqrt((4)^2+(2+3)^2)`
`=sqrt(16+25) = sqrt(41)` units
Hence, k= -1,-3; AP= 5 units for k=-1 and AP=`sqrt(41)` units for k=-3.
APPEARS IN
RELATED QUESTIONS
Find the points of trisection of the line segment joining the points:
(3, -2) and (-3, -4)
Find the coordinates of the point where the diagonals of the parallelogram formed by joining the points (-2, -1), (1, 0), (4, 3) and(1, 2) meet
In what ratio does the point (−4, 6) divide the line segment joining the points A(−6, 10) and B(3,−8)?
Find the points on the y-axis which is equidistant form the points A(6,5) and B(- 4,3)
If p(x , y) is point equidistant from the points A(6, -1) and B(2,3) A , show that x – y = 3
Points P, Q, R and S divide the line segment joining the points A(1,2) and B(6,7) in five equal parts. Find the coordinates of the points P,Q and R
`"Find the ratio in which the poin "p (3/4 , 5/12) " divides the line segment joining the points "A (1/2,3/2) and B (2,-5).`
In what ratio does the point C (4,5) divides the join of A (2,3) and B (7,8) ?
If `P(a/2,4)`is the mid-point of the line-segment joining the points A (−6, 5) and B(−2, 3), then the value of a is
Two points having same abscissae but different ordinate lie on
The distance of the point P (4, 3) from the origin is
Find the ratio in which the line segment joining the points A(3, −3) and B(−2, 7) is divided by the x-axis. Also, find the coordinates of the point of division.
If the points A(1, –2), B(2, 3) C(a, 2) and D(– 4, –3) form a parallelogram, find the value of a and height of the parallelogram taking AB as base.
If the centroid of the triangle formed by points P (a, b), Q(b, c) and R (c, a) is at the origin, what is the value of a + b + c?
The distance between the points (cos θ, 0) and (sin θ − cos θ) is
If three points (0, 0), \[\left( 3, \sqrt{3} \right)\] and (3, λ) form an equilateral triangle, then λ =
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.
Find the coordinates of the point of intersection of the graph of the equation x = 2 and y = – 3
Assertion (A): The point (0, 4) lies on y-axis.
Reason (R): The x-coordinate of a point on y-axis is zero.
Assertion (A): Mid-point of a line segment divides the line segment in the ratio 1 : 1
Reason (R): The ratio in which the point (−3, k) divides the line segment joining the points (− 5, 4) and (− 2, 3) is 1 : 2.
