Respuesta :
Answer:
The coordinate of point B is ( [tex]x_2[/tex] , [tex]y_2[/tex] ) = 7 , 11
Step-by-step explanation:
Given as :
The coordinate of point A = [tex]x_1[/tex] , [tex]y_1[/tex] = - 2 , 4
The coordinate of point M = [tex]x_3[/tex] , [tex]y_3[/tex] = 2.5 , 3.5
Let The coordinate of point B = [tex]x_2[/tex] , [tex]y_2[/tex]
where M is the mid-point of the line joining points A and B
So, from mid-point theorem
[tex]x_3[/tex] = [tex]\dfrac{x_1 + x_2}{2}[/tex]
Or, 2.5 = [tex]\dfrac{ -2 + x_2}{2}[/tex]
Or, 2.5 × 2 = - 2 + [tex]x_2[/tex]
Or, [tex]x_2[/tex] = 5 + 2
∴ [tex]x_2[/tex] = 7
Similarly
[tex]y_3[/tex] = [tex]\dfrac{y_1 + y_2}{2}[/tex]
Or, 2.5 = [tex]\dfrac{ 4 + y_2}{2}[/tex]
Or, 3.5 × 2 = 4 + [tex]y_2[/tex]
Or, [tex]y_2[/tex] = 7 + 4
∴ [tex]y_2[/tex] = 11
So, The coordinate of point B = ( [tex]x_2[/tex] , [tex]y_2[/tex] ) = 7 , 11
Hence, The coordinate of point B is ( [tex]x_2[/tex] , [tex]y_2[/tex] ) = 7 , 11 Answer
