Question

the mid point of the line segment joining the points A(1,7) and B(-5,-3) is​

Answer 1

let M be the mid point of yhe line segment joining the points A and B

here,

let the point on x- axis be 'X'

point ony-axis be 'y'

so,M(x,y) is the mid point

formula to find mid point is

M=(X1 +X2/2 , Y1+Y2/2)

where X1=1 and X2=-5

and Y1=7 and Y2=-3

then,

m=[1 +(-5)/2 , 7+(-3)/2]

m=[1-5/2 , 7-3/2]

m=[-4/2,4/2]

after calculation

m=[-2,2]

therfore,

mid point of points A(1,7) and B(-5,-3) is(-2,2)

Answer 2

Solution!!

The concept of co-ordinate geometry has to be used here.

Let P be the mid-point of the line segment joining the points A(x₁ , y₁) and B(x₂ , y₂). Required to find the co-ordinates of P. Suppose P = (x , y).

Given:-

A = (1 , 7)

B = (-5 , -3)

Now,

Mid-point = ((x₁ + x₂)/2 , (y₁ + y₂)/2)

P(x , y) = ((1 + (-5))/2 , (7 + (-3))/2)

P(x , y) = (-4/2 , 4/2)

P(x , y) = (-2 , 2)

The mid point of the line segment joining the points A(1,7) and B(-5,-3) is (-2 , 2).

More information:-

For any two given points in a co-ordinate (Cartesian) plane, the knowledge of co-ordinate geometry may be used to find:

• the distance between the given points,

• the co-ordinates of a given point which divides the line joining the given points in a given ratio,

• the co-ordinates of the mid-point of the line segment joining the two given points,

• equation of the line through the given points,

• equation of the perpendicular bisector of the line segment obtained on joining the given two points, etc.