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Mathematics

Grade9

Easy

Question

Find the midpoint of a line segment with endpoints at (0, 1) and (5, 7)?

(1, 1)
$(\frac{5}{2}, 4)$
$(\frac{5}{2}, \frac{5}{2})$
$(\frac{5}{2}, \frac{9}{2})$

hint Hint:

The formula to find midpoint of line segment bounded by two points and is $open parentheses fraction numerator x subscript 1 end subscript plus x subscript 2 end subscript over denominator 2 end fraction comma fraction numerator y subscript 1 end subscript plus y subscript 2 end subscript over denominator 2 end fraction close parentheses$

The correct answer is: $open parentheses fraction numerator 5 over denominator 2 end fraction comma 4 close parentheses$

The midpoint of a line segment is halfway between the two x values and halfway between the two y values. Mathematically, that would be the average of each coordinate:
$open parentheses fraction numerator x subscript 2 end subscript plus x subscript 1 end subscript over denominator 2 end fraction comma fraction numerator y subscript 2 end subscript plus y subscript 1 end subscript over denominator 2 end fraction close parentheses$
Plug in the (x, y) values from the given points and solve.
$open parentheses fraction numerator 5 plus 0 over denominator 2 end fraction comma fraction numerator 7 plus 1 over denominator 2 end fraction close parentheses$
$open parentheses fraction numerator 5 over denominator 2 end fraction comma fraction numerator 8 over denominator 2 end fraction close parentheses$
We can simplify the fraction to get the final answer.
$open parentheses fraction numerator 5 over denominator 2 end fraction comma 4 close parentheses$
Therefore, the midpoint of a line segment with endpoints at (0, 1) and (5, 7) is $open parentheses fraction numerator 5 over denominator 2 end fraction comma 4 close parentheses$ .

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