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# 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 - Mathematics

MCQ

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

#### Options

• (0, 2)

•  (3, 0)

•  (0, 3)

•  (2, 0)

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#### Solution

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(xy) 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) .

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#### APPEARS IN

RD Sharma Class 10 Maths
Chapter 6 Co-Ordinate Geometry
Q 33 | Page 65
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