Question

how to solve and the answer?

Answer 1

For both of these problems, we are going to need to use our midpoint formula (the formula uses the coordinates $(x_1, y_1)$ and $(x_2, y_2)$):

$\Bigg(\dfrac{x_1 + x_2}{2} , \dfrac{y_1 + y_2}{2}\Bigg)$

Problem 9:

Let's insert use the information we already know to create an equation which we can solve:

$\Bigg(\dfrac{6 + x_2}{2}, \dfrac{0 + y_2}{2}\Bigg) = (-3, 2)$

Now, let's solve the x-value and y-value of the coordinate independently:

$\dfrac{6 + x_2}{2} = -3 \Rightarrow 6 + x_2 = -6 \Rightarrow x_2 = -12$

$\dfrac{y_2}{2} = 2 \Rightarrow y_2 = 4$

We have found both the x-value and y-value of $S$, making the final answer:

$\boxed{S(-12, 4)}$

Problem 10:

We are going to do the same process as Problem 9.

$\Bigg(\dfrac{7 + x_2}{2} , \dfrac{1 + y_2}{2}\Bigg) = (-1, 5)$

$\dfrac{7 + x_2}{2} = -1 \Rightarrow 7 + x_2 = -2 \Rightarrow x_2 = -9$

$\dfrac{1 + y_2}{2} = 5 \Rightarrow 1 + y_2 = 10 \Rightarrow y_2 = 9$

Our answer is:

$\boxed{W(-9, 9)}$