Question

The coordinators of the midpoint of the line
segment joining the points A (-5, 4) and B (7,
-8) is
a. (1,-2)
b. (-1,2)
c. (2, 1)
d. (1,2)​

Answer 1

$\boxed{\rm{\orange{Given \longrightarrow }}}$

• Coordinates of A = ( - 5 , 4 )
• Coordinates of B = ( 7 , - 8 )

$\boxed{\rm{\red{To\:Find\longrightarrow }}}$

• Midpoint of the line AB

$\boxed{\rm{\pink{solution \longrightarrow }}}$

$\sf Midpoint = \bigg(\dfrac {x_1 +x_2 }{2},\dfrac {y_1 +y_2 }{2} \bigg)$

$\begin{lgathered}\longrightarrow \: \sf x_1 = - 5 \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: x_2 =7 \\ \\ \longrightarrow \: \sf x_1 = 4 \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: x_2 = - 8\end{lgathered}$

Substitute values in formula

$\begin{lgathered}\longrightarrow\sf Midpoint = \bigg(\dfrac { - 5 + 7}{2} \: ,\dfrac {4 +( - 8)}{2} \bigg) \\ \\ \longrightarrow\sf Midpoint = \bigg(\dfrac {2}{2} \: ,\dfrac {-4}{2} \bigg) \\ \\\longrightarrow \boxed{ \sf Midpoint = \bigg(1 \: , \: -2 \bigg)}\end{lgathered}$

$\bf \Large \therefore \: Option \: (1) \: is \: correct$

Answer 2

$\huge\mathcal\red{Answer:}$

a. (1,-2)

Option 1 is the correct answer.