Advertisements
Advertisements
Question
Find the point on x-axis which is equidistant from points A(-1,0) and B(5,0)
Advertisements
Solution
Let P (x ,0) be the point on . x- axis Then
AP = BP ⇒ AP2 = BP2
`⇒ (x+1)^2 + (0-0)^2 = (x-5)^2 +(0-0)^2`
`⇒ x^2 +2x+1=x^2-10x +25`
`⇒ 12x = 24 ⇒ x = 2`
Hence , x = 2
APPEARS IN
RELATED QUESTIONS
Let ABCD be a square of side 2a. Find the coordinates of the vertices of this square when The centre of the square is at the origin and coordinate axes are parallel to the sides AB and AD respectively.
If A and B are (1, 4) and (5, 2) respectively, find the coordinates of P when AP/BP = 3/4.
If the point C ( - 2,3) is equidistant form the points A (3, -1) and Bx (x ,8) , find the value of x. Also, find the distance between BC
Show that the following points are the vertices of a square:
A (0,-2), B(3,1), C(0,4) and D(-3,1)
Show that the points A(3,0), B(4,5), C(-1,4) and D(-2,-1) are the vertices of a rhombus. Find its area.
If the vertices of ΔABC be A(1, -3) B(4, p) and C(-9, 7) and its area is 15 square units, find the values of p
The abscissa and ordinate of the origin are
Points (−4, 0) and (7, 0) lie
If A(−3, 5), B(−2, −7), C(1, −8) and D(6, 3) are the vertices of a quadrilateral ABCD, find its area.
Write the coordinates the reflections of points (3, 5) in X and Y -axes.
Write the ratio in which the line segment doining the points A (3, −6), and B (5, 3) is divided by X-axis.
If A (1, 2) B (4, 3) and C (6, 6) are the three vertices of a parallelogram ABCD, find the coordinates of fourth vertex D.
What is the distance between the points \[A\left( \sin\theta - \cos\theta, 0 \right)\] and \[B\left( 0, \sin\theta + \cos\theta \right)\] ?
The perimeter of the triangle formed by the points (0, 0), (0, 1) and (0, 1) is
If points A (5, p) B (1, 5), C (2, 1) and D (6, 2) form a square ABCD, then p =
Which of the points P(-1, 1), Q(3, - 4), R(1, -1), S (-2, -3), T(-4, 4) lie in the fourth quadrant?
If point P is midpoint of segment joining point A(– 4, 2) and point B(6, 2), then the coordinates of P are ______
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 ______
If y-coordinate of a point is zero, then this point always lies ______.
If the points P(1, 2), Q(0, 0) and R(x, y) are collinear, then find the relation between x and y.
Given points are P(1, 2), Q(0, 0) and R(x, y).
The given points are collinear, so the area of the triangle formed by them is `square`.
∴ `1/2 |x_1(y_2 - y_3) + x_2(y_3 - y_1) + x_3(y_1 - y_2)| = square`
`1/2 |1(square) + 0(square) + x(square)| = square`
`square + square + square` = 0
`square + square` = 0
`square = square`
Hence, the relation between x and y is `square`.
