Question

If p(1,-2) is the midpoint of the line segment joining the points A( 1,k-3) and B(1, k), then the value of k is ……………………….​

Answer 1

Answer:

- 1/2

Step-by-step explanation:

Using mid point formula,

mid point of (a,b) and (c,d) is (a+c/2 , b+d/2).

 So, here,  mid point of AB is,

⇒ (1+1/2  , k-3+k/2 )

⇒ (1 , 2k-3/2)

    In question it is given that the mid point is (1 , - 2).

⇒ (1 , 2k - 3/2)  = (1 , - 2)

          ⇒ 2k-3/2  = - 2

          ⇒ 2k - 3 = - 4

          ⇒ 2k = -4 + 3

          ⇒ k = -1/2

Answer 2

Given:

• p (1, -2) is mid point of line segment joining A( 1, k-3) and B(1,k)

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Need to Find :

• value of k=?

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Solution:

We know for a point to be midpoint,

$(x,y) = ( \dfrac{x1 + x2}{2}, \dfrac{y1 + y2}{2} )$

$\implies \:( 1 ,- 2 )= \dfrac{1 + 1}{2} , \dfrac{k - 3 + k}{2}$

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Solving separately,

$- 2 = \dfrac{2k - 3}{2}$

$\implies \: - 4 = 2k - 3$

$\implies \: 2k = - 1$

$\red{\large{\bold{ \implies \: k = \dfrac{ - 1}{2}}}}$