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).

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