### Video Transcript

Given the point π΄ at two, one and
the point πΆ at negative eight, negative nine, what are the coordinates of π΅, if πΆ
is the midpoint of π΄π΅ where π΄π΅ is a segment?

So if we have a segment π΄π΅ and πΆ
is the midpoint, the distance from π΄ to πΆ would be equal to the distance from πΆ
to π΅. There is a formula to find this
midpoint. So if your midpoint is a point π₯
comma π¦, you need to take the two end points, add the π₯s together, divide by two,
add the π¦s together, divide by two. So this means π΄ would be our π₯
one, π¦ one point, our first point. And then π΅ would be our π₯ two, π¦
two point, our second point. And πΆ would be the midpoint, the
π₯, π¦.

So letβs go ahead and use this
formula and solve for π΅. So first, πΆ is negative eight,
negative nine. And now weβll plug π΄ into the π₯
one, π¦ one. And from here we can solve for π₯
two, π¦ two which is our π΅ 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 π¦ two, whatever that is, and dividing by two. So letβs set negative eight equal
to two plus π₯ two divided by two. And letβs also take negative nine
equal to one plus π¦ two divided by two.

So letβs first begin by solving for
π₯ two. So letβs multiply both sides by
two. So we have negative 16 is equal to
two plus π₯ two. So now letβs subtract two from both
sides. So π₯ two is equal to negative
18.

Now letβs solve for π¦ two. After multiplying both sides by
two, we get negative 18 equals one plus π¦ two. Now letβs subtract one from both
sides. So π¦ two is equal to negative
19.

Since π΅ has the coordinates π₯
two, π¦ two, π΅ will be located at negative 18, negative 19.