Question

If (-1,1),is the mid point of a line segment joining (-3,b) and (a,4) then find ab​

Answer 1

Answer:

Midpoint coordinates = (-1,1)

Coordinates of points making the line = (-3,b) and (a,4)

Midpoint formula : (x1+x2)/2 and (y1+y2)/2.

So, (x1+x2)/2 = -1

⇒ (-3+a)/2 = -1

⇒ -3+a = -1×2

⇒ -3+a = -2

⇒ a = -2+3

⇒ a = 1

And, (y1+y2)/2 = 1

⇒ (b+4)/2 = 1

⇒ b+4 = 1×2

⇒ b+4 = 2

⇒ b = 2-4

⇒ b = -2

So, the values of a = 1 and b = -2.

Answer 2

Answer:

let the midpoint be (x,y)=(-1,1)

let A(X1,y1)=(-3,b) and B(X2,Y2)=(a,4) are the end point of line segment AB.

by midpoint formula,

midpoint(x,y)={(X1+X2)/2},{(Y1+Y2)/2}

=>(-1,1)={(-3+a)/2},{(b+4)/2}

=>-1=(-3+a)/2, 1=(b+4)/2

=>-2=-3+a, 2=b+4

=>-3+a=-2,b+4=2

=>a=-2+3,b=2-4

=>a=1,b=-2

Hence, the value of a and b are 1 and -2 respectively.