Respuesta :
Answer:
The option B) is correct
Therefore the coordinate of B[tex](x_2,y_2)[/tex] is (6,-3)
Step-by-step explanation:
Given that the midpoint of segment AB is (4, 2). The coordinates of point A is (2, 7).
To Find the coordinates of point B:
- Let the coordinate of A be [tex](x_1,y_1)[/tex] is (2,7) respectively
- Let the coordinate of B be [tex](x_2,y_2)[/tex]
- And Let M(x,y) be the mid point of line segment AB is (4,2) respectively
- The mid-point formula is
[tex]M(x,y)=(\frac{x_1+x_2}{2},\frac{y_1+y_2}{2})[/tex]
- Now substitute the coordinates int he above formula we get
- [tex](4,2)=(\frac{2+x_2}{2},\frac{7+y_2}{2})[/tex]
- Now equating we get
[tex]4=\frac{2+x_2}{2}[/tex] [tex]2=\frac{7+y_2}{2}[/tex]
Multiply by 2 we get Multiply by 2 we get
[tex]4(2)=2+x_2[/tex] [tex]2(2)=7+y_2[/tex]
[tex]8=2+x_2[/tex] [tex]4=7+y_2[/tex]
Subtracting 2 on both
the sides Subtracting 7 on both the sides
[tex]8-2=2+x_2-2[/tex] [tex]4-7=7+y_2-7[/tex]
[tex]6=x_2[/tex] [tex]-3=y_2[/tex]
Rewritting the above equation Rewritting the equation
[tex]x_2=6[/tex] [tex]y_2=-3[/tex]
