Answer:
[tex]B(x,y) =(-7,6)[/tex]
Step-by-step explanation:
Given
[tex]A = (-10,4)[/tex]
[tex]D = (2,12)[/tex]
Required
Determine the coordinates of B
C is the midpoint of AD. So, we calculate the coordinates of C, first.
[tex]C(x,y) = (\frac{x_1+x_2}{2},\frac{y_1+y_2}{2})[/tex]
Where:
[tex]A = (-10,4)[/tex] --- [tex](x_1,y_1)[/tex]
[tex]D = (2,12)[/tex] --- [tex](x_2,y_2)[/tex]
So, we have:
[tex]C(x,y) = (\frac{x_1+x_2}{2},\frac{y_1+y_2}{2})[/tex]
[tex]C(x,y) = (\frac{-10+2}{2},\frac{4+12}{2})[/tex]
[tex]C(x,y) = (\frac{-8}{2},\frac{16}{2})[/tex]
[tex]C(x,y) = (-4,8)[/tex]
So, the coordinates of C is (-4,8)
The midpoint of AC is B.
So, we calculate the coordinates of B using:
[tex]B(x,y) = (\frac{x_1+x_2}{2},\frac{y_1+y_2}{2})[/tex]
Where:
[tex]A = (-10,4)[/tex] --- [tex](x_1,y_1)[/tex]
[tex]C(x,y) = (-4,8)[/tex] --- [tex](x_2,y_2)[/tex]
So, we have:
[tex]B(x,y) = (\frac{x_1+x_2}{2},\frac{y_1+y_2}{2})[/tex]
[tex]B(x,y) =(\frac{-10-4}{2},\frac{4+8}{2})[/tex]
[tex]B(x,y) =(\frac{-14}{2},\frac{12}{2})[/tex]
[tex]B(x,y) =(-7,6)[/tex]
Hence, the coordinates of B is (-7,6)
None of the options is correct.
