Video: Finding the Coordinates of a Point Using the Midpoint Formula

Video Transcript

Given the point 𝐴 at two, one and the point 𝐶 at negative eight, negative nine, what are the coordinates of 𝐵, if 𝐶 is the midpoint of 𝐴𝐵 where 𝐴𝐵 is a segment?

So if we have a segment 𝐴𝐵 and 𝐶 is the midpoint, the distance from 𝐴 to 𝐶 would be equal to the distance from 𝐶 to 𝐵. There is a formula to find this midpoint. So if your midpoint is a point 𝑥 comma 𝑦, you need to take the two end points, add the 𝑥s together, divide by two, add the 𝑦s together, divide by two. So this means 𝐴 would be our 𝑥 one, 𝑦 one point, our first point. And then 𝐵 would be our 𝑥 two, 𝑦 two point, our second point. And 𝐶 would be the midpoint, the 𝑥, 𝑦.

So let’s go ahead and use this formula and solve for 𝐵. So first, 𝐶 is negative eight, negative nine. And now we’ll plug 𝐴 into the 𝑥 one, 𝑦 one. And from here we can solve for 𝑥 two, 𝑦 two which is our 𝐵 point. So, so negative eight would be the result of taking two plus 𝑥 two, whatever that is, and dividing by two. And negative nine would be the result of taking one plus 𝑦 two, whatever that is, and dividing by two. So let’s set negative eight equal to two plus 𝑥 two divided by two. And let’s also take negative nine equal to one plus 𝑦 two divided by two.

So let’s first begin by solving for 𝑥 two. So let’s multiply both sides by two. So we have negative 16 is equal to two plus 𝑥 two. So now let’s subtract two from both sides. So 𝑥 two is equal to negative 18.

Now let’s solve for 𝑦 two. After multiplying both sides by two, we get negative 18 equals one plus 𝑦 two. Now let’s subtract one from both sides. So 𝑦 two is equal to negative 19.

Since 𝐵 has the coordinates 𝑥 two, 𝑦 two, 𝐵 will be located at negative 18, negative 19.