Question

BC has a midpoint at M(6, 6). Point C is at (2, 10). Find the coordinates of point B.

Answer 1

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 $(\frac{x_1 + x_2}{2}, \frac{y_1+ y_2}{2})$, where $(x_1, y_1)$ and $(x_2 , y_2)$ are points. In this case, the point C has the values of $(x_1, y_1)$, and B has the values of $(x_2 , y_2)$

We know that coordinates of M equal $(\frac{x_1 + x_2}{2}, \frac{y_1+ y_2}{2})$

In other words,

$\frac{x_1 + x_2}{2} = 6\\ \frac{y_1+ y_2}{2}=6$

Let's plug 2 for $x_1$ and 10 for $y_1$

So:

$\frac{2 + x_2}{2} = 6\\ \frac{10+ y_2}{2}=6$

Multiply both sides by 2

${2 + x_2} = 12\\{10+ y_2} =12$

Subtract 2 from both sides in the first equation to find the value of $x_2$:

$x_2=10$

Now, for the second equation, subtract 10 from both sides to find the value of $y_2$

$y_2=2$

Now substitute these values for $(x_2, y_2)$

$(x_2, y_2)=(10,2)$

So the coordinates of point B are (10, 2)

Hope this helps!