Question

The mid-points of the line-segments joining the points (-2,4) and (6,10) is * a) (2,5) b) (2,7) c) (3,7) d) (3,9)

Answer 1

AnsWer :

b) ( 2 , 7 )

SolutioN :

Let's,

• Point be
• A( - 2 , 4 )
• B( 6 , 10 )

Now, We know ( Mid-point Formula )

$\tt \dagger \: \: \: \: \: \Bigg[ \dfrac{ x_1 + x_2}{2} \: \: \: , \: \: \: \dfrac{ y_1 + y_2}{2}\Bigg]$

Where as,

• x1 = - 2.
• x2 = 6.
• y1 = 4.
• y2 = 10.

For, x

→ x = - 2 + 6 / 2 .

→ x = 4 / 2.

→ x = 2.

$\rule{100}2$

For y.

→ y = 4 + 10 / 2.

→ y = 14 / 2.

→ y = 7.

$\rule{100}2$

SO,

The mid-points of the line-segments joining the points A and B is ( x , y ) → ( 2 , 7 )

$\rule{200}3$

SomE InformatioN :

→ Mid-point Formula :

$\tt \dagger \: \: \: \: \: \Bigg[ \dfrac{ x_1 + x_2}{2} \: \: \: , \: \: \: \dfrac{ y_1 + y_2}{2}\Bigg]$

→ Section Formula :

$\tt \dagger \: \: \: \: \: \Bigg[ \dfrac{ m_1x_2+ m_2x_1}{m_1+m_2}\Bigg]$