Question

find the coordinates of the mid point of the line segment joining the points. ( 0,5 ) and (10,-
1)​

Answer 1

Answer:

0+10/2=10/2=5

5+(-1)/2=5-1/2=4/2=2

(5,2) are the coordinates.

Explanation:

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Answer 2

Given :

• The coordinates of points joining the line segment are ( 0, 5 ) and ( 10 , -1 )

To find :

• The coordinates of the midpoint of the line segment

Formula used :

The midpoint (x, y) of a line segment joining the line segment joining the points (x₁ , y₁) and (x₂ , y₂) is given by ,

$\boxed {\rm{(x , y) = \bigg(\frac{x_1 + x_2}{2} \: , \: \frac{y_1 + y_2}{2} \bigg)}}$

Figure :

$\setlength{\unitlength}{1.5cm}\begin{picture}(6, 6)\thicklines\put(0, 0){\line(1, 0){5}}\put( - 0.3,-0.4){\bf (0,5)}\put(4.8,-0.4){\bf (10, - 1)}\put(2.2,-0.4){\bf(x,y)}\put(2.4, - 0.1){\line(0,1){0.2}} \put( - 0.1,0){ \circle*{0.1}} \put(4.9,0){ \circle*{0.1}}\end{picture}$

Solution :

Let the coordinates of the midpoint of the line segment joining the points (0,5) and (10,-1) be (x,y)

We have ,

Coordinates of points joining the line segment as , (0,5) and (10,-1)

By comparing the coordinates we get ,

• x₁ = 0 , x₂ = 10
• y₁ = 5 , y₂ = -1

Now By applying the formulae ,

$: \implies \rm (x,y) = \bigg( \dfrac{0 + 10}{2} \: , \: \dfrac{5 + ( - 1)}{2} \bigg) \\ \\ : \implies \rm \: (x,y) = \bigg( \frac{10}{2} \: , \: \frac{5 - 1}{2} \bigg) \\ \\ : \implies \rm \: (x,y) = \bigg( 5 \: , \: \frac{4}{2} \bigg) \\ \\ : \implies \rm \: (x,y) = (5,2)$

Hence , The coordinates of the line segment joining the points (0,5) and (10,-1) is (5,2).