Question

if p(x, 3) lies on perpendicular bisector of the line segment joining the points A (4,8) and B ( - 4,0)

Answer 1

Answer:

x = 1

Step-by-step explanation:

Hi,

Given points are A ( 4, 8) and B ( -4, 0)

Let midpoint of A and B be D

Hence, the coordinates of the midpoint of AB, D will be (0, 4).

Let the Slope of the line AB be m = (8 - 0)/4 + 4 = 1.

Since slope of line AB is 1, any line perpendicular to AB will have slope -1/1

= -1

Now consider line PD , slope of line PD = (-1/x)

But slope of PD = -1 since it is perpendicular to AB

Thus, -1/x = -1

⇒ x = 1

Hope, it helped !

Answer 2

Answer:

Step-by-step explanation:

since point p(x,3) lies on the perpendicular bisector AB .

=> AP = BP

by using distance formula ,

we get

(4-x)^2 + (8-3)^2 = (x+4)^2 + (3-0)^2

=> 16 + x^2 -8x + 25 = x^2 + 16 + 8x +9

=> -16x = -16

=> x = 1

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