Advertisements
Advertisements
प्रश्न
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
विकल्प
(0, 2)
(3, 0)
(0, 3)
(2, 0)
Advertisements
उत्तर
TO FIND: The coordinates of a point on x axis which lies on perpendicular bisector of line segment joining points (7, 6) and (−3, 4).
Let P(x, y) be any point on the perpendicular bisector of AB. Then,
PA=PB
`sqrt((x -7)^2 + (y -6)^2) = sqrt((x-(-3))^2+(y-4)^2)`
`(x-7)^2+ (y - 6)^2 = (x +3)62 + (y-4)^2`
`x^2 - 14x + 49 +y^2 - 12y +36 = x^2 +6x +9 +y^2 -8y + 16`
-14x - 6x - 12y - 8y + 49 +36 -9 - 16 = 0
- 20x + 20y + 60 = 0
x - y - 3 = 0
x - y = 3
On x-axis y is 0, so substituting y=0 we get x= 3
Hence the coordinates of point is (3,0) .
APPEARS IN
संबंधित प्रश्न
On which axis do the following points lie?
Q(0, -2)
Two vertices of an isosceles triangle are (2, 0) and (2, 5). Find the third vertex if the length of the equal sides is 3.
Prove that (4, 3), (6, 4) (5, 6) and (3, 5) are the angular points of a square.
Prove that the points A(-4,-1), B(-2, 4), C(4, 0) and D(2, 3) are the vertices of a rectangle.
If the coordinates of the mid-points of the sides of a triangle be (3, -2), (-3, 1) and (4, -3), then find the coordinates of its vertices.
Points P, Q, and R in that order are dividing line segment joining A (1,6) and B(5, -2) in four equal parts. Find the coordinates of P, Q and R.
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 points A (2,3), B (4,k ) and C (6,-3) are collinear, find the value of k.
Point P(x, 4) lies on the line segment joining the points A(−5, 8) and B(4, −10). Find the ratio in which point P divides the line segment AB. Also find the value of x.
A point whose abscissa and ordinate are 2 and −5 respectively, lies in
The distance of the point P (4, 3) from the origin is
If the point P(x, 3) is equidistant from the point A(7, −1) and B(6, 8), then find the value of x and find the distance AP.
If the points P, Q(x, 7), R, S(6, y) in this order divide the line segment joining A(2, p) and B(7, 10) in 5 equal parts, find x, y and p.
Find the value of k, if the points A (8, 1) B(3, −4) and C(2, k) are collinear.
Write the perimeter of the triangle formed by the points O (0, 0), A (a, 0) and B (0, b).
If P (x, 6) is the mid-point of the line segment joining A (6, 5) and B (4, y), find y.
The distance between the points (a cos 25°, 0) and (0, a cos 65°) is
If x is a positive integer such that the distance between points P (x, 2) and Q (3, −6) is 10 units, then x =
