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

Answer:

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

Step-by-step 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 = $(\frac{x1 + x2}{2} , \frac{y1 + y2}{2} )$

⇒$( -2 , 2 ) = ( \frac{-7 + x}{2} , \frac{1 + y}{2} )$

Finding the value of x :                    

⇒$-2 = \frac{-7 + x}{2}$

Do cross multiplication                

⇒$-4 = -7 + x$

⇒$-7 + x = -4$

⇒$x = -4 + 7$

⇒$x = 3$

Now, finding the value of y

⇒$2 = \frac{1+y}{2}$

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!

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