Question

Point M is the midpoint of AB. The coordinates of point A are (−7, 1) and the coordinates of M are (−2, 2). What are the coordinates of point B?

Answer 1

`\huge{\boxed{\sf{ ( 3 , 3 ) }}}`

Explanation:

Co-ordinates of point A = ( -7 , 1 )

Co-ordinates of point M = ( -2 , 2 )

Let the co-ordinates of point B be ( x , y )

A ( -7 , 1 )
`\longrightarrow` ( x1 , y1 )

B ( x , y )
`\longrightarrow` ( x2 , y2 )

Now,

Midpoint =
`((x1 + x2)/(2) , (y1 + y2)/(2) )`

⇒
`( -2 , 2 ) = ( (-7 + x)/(2) , (1 + y)/(2) )`

Finding the value of x :

⇒
`-2 = (-7 + x)/(2)`

Do cross multiplication

⇒
`-4 = -7 + x`

⇒
`-7 + x = -4`

⇒
`x = -4 + 7`

⇒
`x = 3`

Now, finding the value of y

⇒
`2 = (1+y)/(2)`

Do cross multiplication

⇒
`4 = 1+y`

⇒
`1+y = 4`

⇒
`y = 4 - 1`

⇒
`y = 3`

Hence, The co-ordinates of point B = ( 3 , 3 )

Hope I helped!

Best regards!

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