Question

if C is the midpoint of the line segment joining A(3,4) and b(7,6) then the coordinates of the C are​

Answer 1

Here we apply the section formula, i. e. if a point C(x,y) divides the line segment AB joining the points A(x

1

,y

1

)&B(x

2

,y

2

) in the ratio m:n then we have

x=

m+n

nx

1

+mx

2

&y=

m+n

ny

1

+my

2

.

Let the point is C( x,y), Which divides AB in the ratio of 2:1.

Then the coordinates of C are given by

x=

2+1

(2×2)+(−3×1)

=

3

1

y=

3

(2×1)+(1×4)

=2

C≡(

3

1

,2)

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Answer 2

Given :

C is the midpoint of the line segment joining A(3,4) and b(7,6).

To find :

The coordinates of the C.

Solution :

we know that,

The coordinates of the mid point C of the joining A(x₁, y₁) and B(x₂, y₂) is

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

By substituting the values in the formula,

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

$\dashrightarrow \sf C =\bigg( \dfrac{3 + 7}{2} , \dfrac{7 + 6}{2} \bigg)$

$\dashrightarrow \sf C =\bigg( \dfrac{10}{2} , \dfrac{13}{2} \bigg)$

$\dashrightarrow \sf C =\bigg( 5 , \dfrac{13}{2} \bigg)$

$\dashrightarrow \sf C =( 5 , 6.5)$

Thus, the coordinates of C is (5, 6.5).