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

Given 𝐴 (2, 1) and 𝐢 (βˆ’8, βˆ’9), what are the coordinates of 𝐡, if 𝐢 is the midpoint of 𝐴𝐡?

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Video Transcript

Given the point 𝐴 at two, one and the point 𝐢 at negative eight, negative nine, what are the coordinates of 𝐡, if 𝐢 is the midpoint of 𝐴𝐡 where 𝐴𝐡 is a segment?

So if we have a segment 𝐴𝐡 and 𝐢 is the midpoint, the distance from 𝐴 to 𝐢 would be equal to the distance from 𝐢 to 𝐡. There is a formula to find this midpoint. So if your midpoint is a point π‘₯ comma 𝑦, you need to take the two end points, add the π‘₯s together, divide by two, add the 𝑦s together, divide by two. So this means 𝐴 would be our π‘₯ one, 𝑦 one point, our first point. And then 𝐡 would be our π‘₯ two, 𝑦 two point, our second point. And 𝐢 would be the midpoint, the π‘₯, 𝑦.

So let’s go ahead and use this formula and solve for 𝐡. So first, 𝐢 is negative eight, negative nine. And now we’ll plug 𝐴 into the π‘₯ one, 𝑦 one. And from here we can solve for π‘₯ two, 𝑦 two which is our 𝐡 point. So, so negative eight would be the result of taking two plus π‘₯ 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 π‘₯ 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 π‘₯ two. So let’s multiply both sides by two. So we have negative 16 is equal to two plus π‘₯ two. So now let’s subtract two from both sides. So π‘₯ 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 𝐡 has the coordinates π‘₯ two, 𝑦 two, 𝐡 will be located at negative 18, negative 19.

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