Answer:
[tex]\huge{\boxed{\sf{ ( 3 , 3 ) }}}[/tex]
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 ) [tex]\longrightarrow[/tex] ( x1 , y1 )
B ( x , y ) [tex]\longrightarrow[/tex] ( x2 , y2 )
Now,
Midpoint = [tex](\frac{x1 + x2}{2} , \frac{y1 + y2}{2} )[/tex]
⇒[tex]( -2 , 2 ) = ( \frac{-7 + x}{2} , \frac{1 + y}{2} )[/tex]
Finding the value of x :
⇒[tex]-2 = \frac{-7 + x}{2}[/tex]
Do cross multiplication
⇒[tex]-4 = -7 + x[/tex]
⇒[tex]-7 + x = -4[/tex]
⇒[tex]x = -4 + 7[/tex]
⇒[tex]x = 3[/tex]
Now, finding the value of y
⇒[tex]2 = \frac{1+y}{2}[/tex]
Do cross multiplication
⇒[tex]4 = 1+y[/tex]
⇒[tex]1+y = 4[/tex]
⇒[tex]y = 4 - 1[/tex]
⇒[tex]y = 3[/tex]
Hence, The co-ordinates of point B = ( 3 , 3 )
Hope I helped!
Best regards!
~[tex]\text{ TheAnimeGirl}[/tex]
