Answer :
Answer:
B = (-4, 4)
Step-by-step explanation:
To find the coordinate of B where C is the midpoint of AB and the values of A (0, 0) and C (-2, 2), we use this formula:
[tex]\boxed{(x_{mid},y_{mid})=\left(\frac{x_1+x_2}{2},\frac{y_1+y_2}{2} \right) }[/tex]
where:
- [tex](x_{mid},y_{mid})=\texttt{coordinate of midpoint}[/tex]
- [tex](x_1,y_1)\texttt{ and }(x_2,y_2)=\texttt{coordinates of endpoints}[/tex]
Given:
- endpoint A = (0, 0)
- midpoint C = (-2, 2)
Then:
[tex]\begin{aligned}(x_{C},y_{C})&=\left(\frac{x_A+x_B}{2},\frac{y_A+y_B}{2} \right)\\\\(-2,2)&=\left(\frac{0+x_B}{2},\frac{0+y_B}{2} \right)\\\\(-2,2)&=\left(\frac{x_B}{2},\frac{y_B}{2} \right)\end{aligned}[/tex]
Now, we calculate the [tex]x_B[/tex]:
[tex]\begin{aligned}-2&=\frac{x_B}{2} \\\\x_B&=2(-2)\\\\\bf x_B&=-4\end{aligned}[/tex]
and [tex]y_B[/tex]:
[tex]\begin{aligned}2&=\frac{y_B}{2} \\\\y_B&=2(2)\\\\\bf y_B&=4\end{aligned}[/tex]
Hence the coordinate of B = (-4, 4).
