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Given point 𝐴 has coordinates four, eight and 𝐵 has coordinates six, six, what are the coordinates of the midpoint of line segment 𝐴𝐵?
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We can solve this problem graphically or by using the midpoint formula.
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And it is this method we’ll use first.
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We recall that if points 𝐴 and 𝐵 have coordinates 𝑥 one, 𝑦 one and 𝑥 two, 𝑦 two, respectively, then the midpoint has coordinates 𝑥 one plus 𝑥 two over two, 𝑦 one plus 𝑦 two over two.
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In this question, point 𝐴 has coordinates four, eight, and point 𝐵 has coordinates six, six.
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This means that the midpoint of the line segment 𝐴𝐵 has 𝑥-coordinate equal to four plus six over two and 𝑦-coordinate equal to eight plus six over two.
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Adding four and six gives us 10.
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And dividing this by two gives us five.
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Likewise, eight plus six is equal to 14.
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And dividing this by two gives us seven.
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The midpoint of points 𝐴 and 𝐵 has coordinates five, seven.
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As already mentioned, we could also represent this graphically on the two-dimensional coordinate plane.
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The midpoint of line segment 𝐴𝐵 lies halfway between points 𝐴 and 𝐵 as shown.
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And it is clear from the graph that this lies at the point five, seven.