Find the midpoint of the segment AB  is A(2, 7)   and B (3,-4)

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hala718's profile pic

hala718 | High School Teacher | (Level 1) Educator Emeritus

Posted on

Let M be the mid point of AB

A(2,7)   B(3, -4)

Then we know that:

xM = (xA+xB)/2

==> xM = (2+3)/2 =  2.5

 

ym = (yA+yB)/2

==> yM = (7+ -4)/2 = 3/2 = 1.5

Then the point M is:

M (2.5, 1.5) 

neela's profile pic

neela | High School Teacher | (Level 3) Valedictorian

Posted on

Let the mid point of A(2,7) and B(3,-4)  be P(x,y)

We know that  the x and y coordinates of  any point  P(x,y) that divides  the line joining the points A and B in the ratio m : n is given by:

Px =  (nAx +mBx)/(m+n).

Py = (nAy+mBy)/(m+n).

Therefore , in case of the mid point , m= n = 1.

So  x coordinate ,Px = (Ax+Bx)/(1+1) = (2+ 5)/2 = 7/2.

y coordinate, Py = (Ay+By)/(1+1) = (7-4)/(1+1) = 3/2.

Therefore P(x,y) = (7/2, 3/2) is the mid point of A(2,7) and B(5, -4).

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