Question

1) Find the co-ordinates of point P if P is the midpoint of a line segment AB with A (-4,2) and B (6,2).​

Answer 1

Answer: C(1, 2)

Let the co-ordinates of midpoint be C(x,y) and let A(-4,2) be A(x1, x2) and B(6, 2) be B(x2, y2)

x = x1 + x2/2   -----------Sector formula

  = -4 + 6/2

  = 2/2

  = 1

y = y1 + y2/2   -------------Sector formula

y = 2 + 2/2

y = 4/2

y = 2

So the midpoint is C(1, 2)

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Answer 2

Answer:

AP^2=BP^2

Put p=x

(x+(-4)^2+(y+2)^2=(x+6)^2+(y+2)^2

x^2+16-8x+y^2+4+4y= x^2+36+12x+y^2+4+4y

x^2+16-8x-x^2-36-12x=y^2+4+4y-y^2-4-4y

16-8x-36-12x=0

-20-20x=0

20x=20

x=20/20

x=1

p=1