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Mathematics

Grade9

Easy

Question

If a line has a midpoint at (2, 5), and the endpoints are (0, 0) and (4, y), find the value of y ?

4
2.5
10
5

hint Hint:

The formula to find midpoint of line segment bounded by two points and is $open parentheses fraction numerator x subscript 1 end subscript plus x subscript 2 end subscript over denominator 2 end fraction comma fraction numerator y subscript 1 end subscript plus y subscript 2 end subscript over denominator 2 end fraction close parentheses$ . Equate them with given values to find the value of y.

The correct answer is: 10

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.
$open parentheses fraction numerator 4 plus 0 over denominator 2 end fraction comma fraction numerator y plus 0 over denominator 2 end fraction close parentheses equals left parenthesis 25 right parenthesis$
Now we can solve for the missing value.
$open parentheses fraction numerator 4 over denominator 2 end fraction comma fraction numerator y over denominator 2 end fraction close parentheses equals left parenthesis 25 right parenthesis$
$4 over 2 equals 2$
The x values reduce, so both x values equal 2. Now we need to create a new equation to solve for the y value.
Multiply both sides by 2 to solve.
$y over 2 equals 5 space rightwards double arrow$ y = 10
Therefore, The value of y is 10.

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