Question

If the midpoint of the line segment joining A(x/2,0) and B(x+1,-4) is C(5,-2), then the value of x is
(a) 6 (b) -6 (c)-1 (d)none of these​

Answer 1

The value of x is (a)6.

• A line is drawn between point A and B.
• Point C is the midpoint of the line joining A and B.
• Formula to calculate mid-points is given as -

C(x,y) = ($\frac{x_1+x_2}{2}$,$\frac{y_1+y_2}{2}$)

• Substituting the known values we get,

(5,2)= ($\frac{\frac{x}{2} +x+1}{2}$,$\frac{0-2}{2}$)

• Comparing both sides we get,

5 = $\frac{\frac{x}{2} + x+1}{2}$

10 = \frac{x}{2} + x+1

20 = x + 2x + 2

18 = 3x

x = 6