Answer:
The coordinates of B are (10,2)
Step-by-step explanation:
Hi there!
We know that BC has a midpoint M, with the coordinates (6,6), and the endpoint C, with coordinates (2, 10)
We want to find the coordinates of point B
The midpoint formula is [tex](\frac{x_1 + x_2}{2}, \frac{y_1+ y_2}{2})[/tex], where [tex](x_1, y_1)[/tex] and [tex](x_2 , y_2)[/tex] are points. In this case, the point C has the values of [tex](x_1, y_1)[/tex], and B has the values of [tex](x_2 , y_2)[/tex]
We know that coordinates of M equal [tex](\frac{x_1 + x_2}{2}, \frac{y_1+ y_2}{2})[/tex]
In other words,
[tex]\frac{x_1 + x_2}{2} = 6\\ \frac{y_1+ y_2}{2}=6[/tex]
Let's plug 2 for [tex]x_1[/tex] and 10 for [tex]y_1[/tex]
So:
[tex]\frac{2 + x_2}{2} = 6\\ \frac{10+ y_2}{2}=6[/tex]
Multiply both sides by 2
[tex]{2 + x_2} = 12\\{10+ y_2} =12[/tex]
Subtract 2 from both sides in the first equation to find the value of [tex]x_2[/tex]:
[tex]x_2=10[/tex]
Now, for the second equation, subtract 10 from both sides to find the value of [tex]y_2[/tex]
[tex]y_2=2[/tex]
Now substitute these values for [tex](x_2, y_2)[/tex]
[tex](x_2, y_2)=(10,2)[/tex]
So the coordinates of point B are (10, 2)
Hope this helps!
