Advertisements
Advertisements
Question
If the points p (x, y) is point equidistant from the points A (5, 1)and B (–1, 5), Prove that 3x = 2y
Advertisements
Solution
As per the question, we have
AP = BP
`⇒ sqrt((x -5)^2 +(y-1)^2) = sqrt((x+1)^2 +(y-5)^2)`
`⇒(x-5)^2 +(y-1)^2 = (x+1)^2 +(y-5)^2` (Squaring both sides)
`⇒x^2 - 10x +25 + y^2 -2y +1 = x^2 +2x +1+y^2 -10y+25`
⇒ –10x – 2y = 2x – 10y
⇒ 8y = 12x
⇒ 3x = 2y
RELATED QUESTIONS
Let ABCD be a square of side 2a. Find the coordinates of the vertices of this square when A coincides with the origin and AB and AD are along OX and OY respectively.
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.
Show that the points (−3, 2), (−5,−5), (2, −3) and (4, 4) are the vertices of a rhombus. Find the area of this rhombus.
Show that the points A(5, 6), B(1, 5), C(2, 1) and D(6,2) are the vertices of a square.
Name the quadrilateral formed, if any, by the following points, and given reasons for your answers:
A(-1,-2) B(1, 0), C (-1, 2), D(-3, 0)
In what ratio is the line segment joining A(2, -3) and B(5, 6) divide by the x-axis? Also, find the coordinates of the pint of division.
In what ratio does y-axis divide the line segment joining the points (-4, 7) and (3, -7)?
Find the area of the quadrilateral ABCD, whose vertices are A(−3, −1), B (−2, −4), C(4, − 1) and D (3, 4).
Show that A(-4, -7), B(-1, 2), C(8, 5) and D(5, -4) are the vertices of a
rhombus ABCD.
The area of the triangle formed by the points A(2,0) B(6,0) and C(4,6) is
If the points A(−2, 1), B(a, b) and C(4, −1) ae collinear and a − b = 1, find the values of aand b.
If the distance between the points (3, 0) and (0, y) is 5 units and y is positive. then what is the value of y?
What is the distance between the points \[A\left( \sin\theta - \cos\theta, 0 \right)\] and \[B\left( 0, \sin\theta + \cos\theta \right)\] ?
If the points A (1,2) , O (0,0) and C (a,b) are collinear , then find a : b.
The distance between the points (a cos θ + b sin θ, 0) and (0, a sin θ − b cos θ) is
If A (5, 3), B (11, −5) and P (12, y) are the vertices of a right triangle right angled at P, then y=
The ratio in which (4, 5) divides the join of (2, 3) and (7, 8) is
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
Any point on the line y = x is of the form ______.
Distance of the point (6, 5) from the y-axis is ______.
