Advertisements
Advertisements
प्रश्न
If p(x , y) is point equidistant from the points A(6, -1) and B(2,3) A , show that x – y = 3
Advertisements
उत्तर
The given points are A(6,-1) and B(2,3). The point P(x, y) equidistant from the points A and B So, PA = PB
Also,` (PA)^2 = (PB)^2`
`⇒ (6-x)^2 +(-1-y)^2 = (2-x) ^2 +(3-y)^2`
`⇒ x^2-12x +36+y^2+2y+1=x^2-4x+4+y^2-6y+9`
`⇒x^2 +y^2-12 x +2y +37 = x^2 -4x-6y+13`
`⇒ x^2 +y^2 -12x +2y -x^2 -y^2 +4x +6y = 13-37`
⇒ -8x +8y = -24
⇒-8 (x-y) = -24
`⇒x-y =(-24)/(-8)`
`⇒ x-y = 3`
Hence proved
APPEARS IN
संबंधित प्रश्न
The coordinates of the point P are (−3, 2). Find the coordinates of the point Q which lies on the line joining P and origin such that OP = OQ.
Find the point on x-axis which is equidistant from the points (−2, 5) and (2,−3).
Find the points of trisection of the line segment joining the points:
(3, -2) and (-3, -4)
Determine the ratio in which the straight line x - y - 2 = 0 divides the line segment
joining (3, -1) and (8, 9).
The points A(2, 0), B(9, 1) C(11, 6) and D(4, 4) are the vertices of a quadrilateral ABCD. Determine whether ABCD is a rhombus or not.
Find the coordinates of the midpoints of the line segment joining
P(-11,-8) and Q(8,-2)
Find 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.
If the point P(k - 1, 2) is equidistant from the points A(3, k) and B(k, 5), find the value of k.
Two points having same abscissae but different ordinate lie on
If (a,b) is the mid-point of the line segment joining the points A (10, - 6) , B (k,4) and a - 2b = 18 , find the value of k and the distance AB.
Write the coordinates the reflections of points (3, 5) in X and Y -axes.
If the centroid of the triangle formed by (7, x) (y, −6) and (9, 10) is at (6, 3), then (x, y) =
The coordinates of a point on x-axis which lies on the perpendicular bisector of the line segment joining the points (7, 6) and (−3, 4) are
The line segment joining the points A(2, 1) and B (5, - 8) is trisected at the points P and Q such that P is nearer to A. If P also lies on the line given by 2x - y + k= 0 find the value of k.
Write the equations of the x-axis and y-axis.
Point (0, –7) lies ______.
Which of the points P(0, 3), Q(1, 0), R(0, –1), S(–5, 0), T(1, 2) do not lie on the x-axis?
The perpendicular distance of the point P(3, 4) from the y-axis is ______.
If the vertices of a parallelogram PQRS taken in order are P(3, 4), Q(–2, 3) and R(–3, –2), then the coordinates of its fourth vertex S are ______.
