Question

If the midpoint of the line segment joining A(3,12y) and B(7, y – 3) is C(5, -2), then the value of y is
(a) 1 (b) 2 (c) –1 (d)none of these

Answer 1

Answer:

The formula for the midpoint of a line segment is given as

(x,y) = [ x1+x2/2 , y1+y2/2]

So,

(5,-2) = [ 3+7/2, 12y + y-3/2]

We can clearly see that the equation is being satisfied for the given ordered pair.

So,

Now, to equate the y coordinate

-2 = 13y-3/2

Or,

13y = -1 or, y = -1/13

Hope this helps you !

Answer 2

$\large\underline\mathfrak\purple{\sf{Answer-}}$

Option d) none of these.

$\large\underline\mathfrak\purple{\sf{Formula\:used-}}$

★ By using the mid point formula, we can find the value of y easily.

Mid point formula :

$\sf{x=\dfrac{x_1\:+\:x_2}{2}}$

$\sf{y=\dfrac{y_1\:+\:y_2}{2}}$

$\sf{(x,y)=\dfrac{x_1\:+x_2}{2}}$, $\sf\dfrac{y_1\:+\:y_2}{2}$

★ We can also use sectional formula for finding the value of y.

$\large\underline\mathfrak\purple{\sf{Explanation-}}$

$\sf{(x,y)=\dfrac{x_1\:+\:x_2}{2}}$, $\sf{\dfrac{y_1\:+\:y_2}{2}}$

Putting the values which are given in the question,

$\sf{(5,-2)=\dfrac{3\:+\:7}{2}}$, $\sf{\dfrac{12y\:+\:y-3}{2}}$

For finding the value of y,

$\sf{-2=\dfrac{12y\:+\:y-3}{2}}$

By cross multiplying,

$\implies$ $\sf{2(-2)=(12y+y-3)}$

$\implies$ $\sf{-4=13y-3}$

$\implies$ $\sf{-4+3=13y}$

$\implies$ $\sf{13y=-1}$

$\implies$ $\sf{y=\dfrac{-1}{13}}$

Thus, the correct option is d) none of these.

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