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
Hence, 3x=2y.
APPEARS IN
RELATED QUESTIONS
On which axis do the following points lie?
P(5, 0)
Which point on the y-axis is equidistant from (2, 3) and (−4, 1)?
Find the equation of the perpendicular bisector of the line segment joining points (7, 1) and (3,5).
Find the points of trisection of the line segment joining the points:
(3, -2) and (-3, -4)
Point A lies on the line segment PQ joining P(6, -6) and Q(-4, -1) in such a way that `(PA)/( PQ)=2/5` . If that point A also lies on the line 3x + k( y + 1 ) = 0, find the value of k.
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
The base QR of a n equilateral triangle PQR lies on x-axis. The coordinates of the point Q are (-4, 0) and origin is the midpoint of the base. Find the coordinates of the points P and R.
In what ratio does the point C (4,5) divides the join of A (2,3) and B (7,8) ?
The abscissa and ordinate of the origin are
The abscissa of any point on y-axis is
Find the area of a parallelogram ABCD if three of its vertices are A(2, 4), B(2 + \[\sqrt{3}\] , 5) and C(2, 6).
If \[D\left( - \frac{1}{5}, \frac{5}{2} \right), E(7, 3) \text{ and } F\left( \frac{7}{2}, \frac{7}{2} \right)\] are the mid-points of sides of \[∆ ABC\] , find the area of \[∆ ABC\] .
Write the ratio in which the line segment doining the points A (3, −6), and B (5, 3) is divided by X-axis.
The distance of the point (4, 7) from the x-axis is
If the points P (x, y) is equidistant from A (5, 1) and B (−1, 5), then
Points (1, –1) and (–1, 1) lie in the same quadrant.
Find the coordinates of the point whose abscissa is 5 and which lies on x-axis.
In which quadrant, does the abscissa, and ordinate of a point have the same sign?
The distance of the point (3, 5) from x-axis (in units) is ______.
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.
