Advertisements
Advertisements
Question
If the poin A(0,2) is equidistant form the points B (3, p) and C (p ,5) find the value of p. Also, find the length of AB.
Advertisements
Solution
As per the question
AB = AC
`⇒ sqrt((0-3)^2 +(2-p)^2 ) = sqrt((0-p)^2 + (2-5)^2)`
`⇒ sqrt((-3)^2 +(2-p)^2) = sqrt((-p)^2 + (-3)^2)`
Squaring both sides, we get
`(-3)^2 +(2-p)^2 = (-p)^2 +(-3)^2`
`⇒ 9+4+p^2-4p=p^2+9`
`⇒ 4p =4`
⇒ p=1
Now,
`AB = sqrt((0-3)^2 +(2-p)^2)`
`= sqrt((-3)^2 +(2-1)^2))` (∵p=1)
`=sqrt(9+1)`
`= sqrt(10)` units
Hence, p = 1 and AB =`sqrt(10)` units
APPEARS IN
RELATED QUESTIONS
If the points A(k + 1, 2k), B(3k, 2k + 3) and C(5k − 1, 5k) are collinear, then find the value of k
On which axis do the following points lie?
S(0,5)
The three vertices of a parallelogram are (3, 4) (3, 8) and (9, 8). Find the fourth vertex.
Find the value of k, if the point P (0, 2) is equidistant from (3, k) and (k, 5).
Determine the ratio in which the straight line x - y - 2 = 0 divides the line segment
joining (3, -1) and (8, 9).
If three consecutive vertices of a parallelogram are (1, -2), (3, 6) and (5, 10), find its fourth vertex.
Determine the ratio in which the point (-6, a) divides the join of A (-3, 1) and B (-8, 9). Also, find the value of a.
If the point A (4,3) and B ( x,5) lies on a circle with the centre o (2,3) . Find the value of x.
The midpoint P of the line segment joining points A(-10, 4) and B(-2, 0) lies on the line segment joining the points C(-9, -4) and D(-4, y). Find the ratio in which P divides CD. Also, find the value of y.
Show that A(-4, -7), B(-1, 2), C(8, 5) and D(5, -4) are the vertices of a
rhombus ABCD.
The co-ordinates of point A and B are 4 and -8 respectively. Find d(A, B).
The distance of the point P (4, 3) from the origin is
Write the distance between the points A (10 cos θ, 0) and B (0, 10 sin θ).
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?
what is the value of \[\frac{a^2}{bc} + \frac{b^2}{ca} + \frac{c^2}{ab}\] .
If the points (k, 2k), (3k, 3k) and (3, 1) are collinear, then k
If the centroid of the triangle formed by (7, x) (y, −6) and (9, 10) is at (6, 3), then (x, y) =
Any point on the line y = x is of the form ______.
If the sum of X-coordinates of the vertices of a triangle is 12 and the sum of Y-coordinates is 9, then the coordinates of centroid are ______.
Assertion (A): The point (0, 4) lies on y-axis.
Reason (R): The x-coordinate of a point on y-axis is zero.
