Question

Find the value of c for which point P(c/3, -2) is the midpoint of the line segment the points Q(-5,4) and R(-1,0)​

Answer 1

Answer:

The value of c will be -9

Answer 2

GIVEN:-

• P(c/3, -2) is the midpoint of the line segment the points Q(-5,4) and R(-1,0).

To Find:-

The value of c.

SOLUTION:-

By using the mid point formula,

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

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

It is said that P(c/3, -2) is the mid point of QR.

So,

According to the question,

$\large\Longrightarrow{\sf{\dfrac{c}{3}=\dfrac{x_1+x_2}{2}}}$

$\large\Longrightarrow{\sf{\dfrac{c}{3}=\dfrac{(-5)+(-1)}{2}}}$

$\large\Longrightarrow{\sf{\dfrac{c}{3}=\dfrac{-5-1}{2}}}$

$\large\Longrightarrow{\sf{\dfrac{c}{3}=\dfrac{-6}{2}}}$

By cross multiplication,

$\large\Longrightarrow{\sf{2c=-18}}$

$\large\Longrightarrow{\sf{c=\dfrac{-18}{2}}}$

$\large\therefore\boxed{\sf{c=-9}}$

• Now let's verify it:-

Using the mid point formula,

$\large\Longrightarrow{\sf{\dfrac{-9}{3}=\dfrac{x_1+x_2}{2}}}$

$\large\Longrightarrow{\sf{-3=\dfrac{(-5)+</p><p>(-1)}{2}}}$

$\large\Longrightarrow{\sf{-3=\dfrac{-5-1}{2}}}$

$\large\Longrightarrow{\sf{-3=\dfrac{-6}{2}}}$

$\large\Longrightarrow{\sf{-3=-3}}$

$\large\therefore\boxed{\sf{LHS=RHS}}$

Hence verified.

$\large\pink\therefore\boxed{\sf{\pink{Value\:of\:c\:=-9}}}$