Question

10. Find the co-ordinates of
the mid-point of the line joining the following points :
(i)(2,4), (6,2)
(ii) (0, 2) and (2,-4)
(iii) (a +b, a - b) and (b-a, a +b)
(iv) (3,-5) and (-1,3)
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Answer 1

Step-by-step explanation:

we know,

midpoint formula

(x, y)

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

1)(2,4), (6,2)

(x, y) = [ ( 2 + 6 ) /2 , ( 4 + 2 ) / 2 ]

= [ ( ( 8 ) / 2 ) , ( (6) / 2 ) ]

= ( 4 , 3 )

there for, the coordinates of midpoint joining the points (2,4) and (6,2) are (x, y) = ( 4 , 3 )

_____________________________

2) (0, 2) and (2,-4)

(x, y) = [ ( 0 + 2)/2 , (2 - 4)/2 ]

= [ ( 2 / 2) , ( -2 / 2) ]

= ( 1 , -1 )

there for, the coordinates of midpoint joining the points (0,2) and (2 , -4) are (x, y) = ( 1 , -1)

______________________________

3)(a +b, a - b) and (b-a, a +b)

(x , y)

= [((a+b)+ (a+b))/2,((a -b)+(b-a)) /2]

= [ 2 (a + b) / 2 , ( a - b + b - a) / 2]

= [ (a + b), (0 / 2)]

(x , y)= ((a + b) , 0)

there for, the coordinates of midpoint joining the points (a +b, a - b) and (b-a, a +b) are (x, y) = ((a + b), 0 )

_____________________________

4) (3,-5) and (-1,3)

(x , y) = [ ( 3 - 1)/ 2 , (-5 + 3) /2 ]

= [ ( 2 / 2) , ( -2 / 2 ) ]

= ( 1 , -1)

there for, the coordinates of midpoint joining the points (3,-5) and (-1,3) are (x, y) = (1 , -1)

____________________________

Answer 2

Explanation:

Given Problem:

Find the co-ordinates of  the mid-point of the line joining the following points :

(i) (2,4), (6,2)

(ii) (0, 2) and (2,-4)

(iii) (a +b, a - b) and (b-a, a +b)

(iv) (3,-5) and (-1,3)

Solution:

To Find:

Co-ordinates.

----------------------

Method:

We know that,

Mid-point Formula:

(x,y)

$\implies\dfrac{( x1 + x2 ) }{2},\dfrac{(y1 +,y2)}{2}$

Now,

1. (2,4), (6,2)

x,y = $\dfrac{( 2 + 6 )}{2},\dfrac{( 4 + 2 )}{2}$

$= \dfrac{(8)}{2},\dfrac{(6)}{2}$

$=  ( 4 , 3 )$

Hence,

The

Coordinates of midpoint joining the points:

(2,4) and (6,2) are (x, y) = (4,3)

_______________________________

2. (0, 2) and (2,-4)

According to formula:

(x,y) = $\dfrac{( 0 + 2)}{2},\dfrac{ (2 - 4)}{2}$

$= \dfrac{2}{2},\dfrac{-2}{2}$

$=  ( 1 , -1 )$

Hence,

The

Coordinates of midpoint joining the points:

(0,2) and (2,-4)  (x, y) = ( 1 , -1)

_______________________________

3. (a +b, a - b) and (b-a, a +b)

According to formula:

(x,y) = $\dfrac{(a+b)+ (a+b)}{2},\dfrac{(a -b)+(b-a)}{2}$

$= \dfrac{2 (a + b)}{2},\dfrac{( a - b + b - a)}{2}$

$= (a + b), \dfrac{0}{2}$

(x,y) = [(a + b) , 0]

Hence,

The

Coordinates of midpoint joining the points:

(a +b, a - b) and (b-a, a +b) are (x, y) = [(a + b), 0]

_______________________________

4. (3,-5) and (-1,3)

According to formula:

(x,y) = $\dfrac{( 3 - 1)}{2},\dfrac{(-5 + 3)}{2}$

$= \dfrac{2}{2},\dfrac{-2}{2}$

= (1 ,-1)

Hence,

The

Coordinates of midpoint joining the points:

(3,-5) and (-1,3) are (x, y) = (1 , -1)

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