Question

Please helppppp!! Find the midpoint of the segment with the following end points (-2,7) and (2,3)

Answer 1

`\huge{ \boxed{ \bold{ \tt( \: 0 \: ,5 \: )}}}`

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☞ First, Let's explore about Midpoint :

Midpoint of the segment simply means middle point of a line segment. Formula of Midpoint :

`\boxed{ \sf{(x _( \: m \: ) ,\: y_(m)) = ( (x_(1) + x_(2))/(2) ,\: (y_(1) + y_(2))/(2) )}}`

where ,

• 
  `( \sf{x_( \: m \: ) ,\: y _( \: m \: ))}` = co-ordinates of the midpoint

• 
  `( \sf{ x_( \: 1 \: ), \: y_( \: 1 \: )})` = co-ordinates of the first point

• 
  `\sf{(x _( \: 2 \: ) ,\: y_( \: 2 \: ))}` = co-ordinates of the second point

The Midpoint Formula is used to find the exact center point between two defined points in a line segment. The Midpoint formula is quite simple , so you should easily be able to remember it. It won't matter which point you pick to be the 'first" point you plug in. Just make sure that you're adding both an x to an x and a y to a y. Hence, keep in mind , in order to find the midpoint of a line segment, the first step is to add both ' x - co-ordinates' and divide it by 2 and then the second step is to add both ' y - co-ordinates ' and divide it by 2.

Now, Let's solve it!

☯ Question :

• Find the midpoint of the segment with the following end points ( - 2 , 7 ) and ( 2 , 3 ).

☯ Step - by - step explanation :

Let P ( x , y ) divide the line joining the points A ( - 2 , 7 ) and B ( 2 , 3 ). Now, let :

• A ( - 2 , 7 ) → ( x₁ , y₁ )
• B ( 2 , 3 ) → ( x₂ , y₂ )

Apply midpoint formula , then plug the values and lastly simplify it :

`\sf{ midpoint \: = \: ( (x _( \: 1 \: ) + x _( \: 2 \: ))/(2) ,  \: (y_( \: 1 \: ) + y _( \: 2\: ))/(2) })`

➺
`\sf{midpoint = ( ( - 2 + 2)/(2),  \: (7 + 3)/(2) )}`

➺
`\sf{midpoint = ( (0)/(2) ,  \: (10)/(2) )}`

➺
`\boxed{ \sf{ midpoint = ( \: 0 \: , 5})}`

Hence , The midpoint of the segment with the end points A ( - 2 , 7 ) and B ( 2 , 3 ) is ( 0 , 5 ) .

Hope I helped!

Have a wonderful time ッ

~TheAnimeGirl ♡

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