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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?
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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΅.
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There is a formula to find this midpoint.
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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.
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So this means π΄ would be our π₯ one, π¦ one point, our first point.
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And then π΅ would be our π₯ two, π¦ two point, our second point.
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And πΆ would be the midpoint, the π₯, π¦.
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So letβs go ahead and use this formula and solve for π΅.
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So first, πΆ is negative eight, negative nine.
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And now weβll plug π΄ into the π₯ one, π¦ one.
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And from here we can solve for π₯ two, π¦ two which is our π΅ point.
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So, so negative eight would be the result of taking two plus π₯ two, whatever that is, and dividing by two.
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And negative nine would be the result of taking one plus π¦ two, whatever that is, and dividing by two.
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So letβs set negative eight equal to two plus π₯ two divided by two.
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And letβs also take negative nine equal to one plus π¦ two divided by two.
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So letβs first begin by solving for π₯ two.
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So letβs multiply both sides by two.
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So we have negative 16 is equal to two plus π₯ two.
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So now letβs subtract two from both sides.
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So π₯ two is equal to negative 18.
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Now letβs solve for π¦ two.
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After multiplying both sides by two, we get negative 18 equals one plus π¦ two.
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Now letβs subtract one from both sides.
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So π¦ two is equal to negative 19.
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Since π΅ has the coordinates π₯ two, π¦ two, π΅ will be located at negative 18, negative 19.