Question

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 what

Answer 1

Answer:

(0,3)

Step-by-step explanation:

Equation of the line passing through the points (7,6) and (-3,4)

be,

Slope of the line = 4-6/-3-7 = 1/5

Equation will be ..

y - 6 = 1/5 ( x - 7 )

5y - 30 = x - 7

5y -x -23 = 0

x - 5y + 23 = 0

And we know that the Perpendicular bisector of the line will pass through the mid point joining the points whose coordinates are :

By Section formula and here m = n = 1 ,

x = 7 + (-3) / 2 =  2         y = (6 + 4) / 2 = 5

⇒ ( 2,5)

Now , the slope of the perpendicular bisector will be:

-5, because we know that if two lines a perpendicular on each other the multiplication of their slopes is always equal to -1

so , m1 * m2 = -1

   ⇒ 1/5 * m2 = -1

   ⇒ m2 = -5

So the equation of the perpendicular bisector will be: {passing through (2,5) and have slope ( -5) }

y - 5 = -5 ( x- 2)

y- 5 = -5x + 10

5x + y - 15 = 0

We have to find the coordinate of the point on X - axis that means the coordinates of the point be like ( x , 0 )

And it lies on that line so if we put the value of x and y in the equation it will be equal to 0

So putting x = x and y = 0

We have, 5x + y - 15 = 0

             ⇒ 5 (x) + 0 -15 = 0

             ⇒ 5x -15 = 0

             ⇒ x = 3

Hope it will help ......

Thanks.....

Answer 2

Step-by-step explanation:

answer is (3,0) I hope it will help you