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Mathematics

Grade9

Easy

Question

What is the radius when the endpoints of the diameter are (5, 6) and (1, 2)?

$\sqrt{2}$
$2 \sqrt{2}$
$3 \sqrt{2}$
$8 \sqrt{2}$

hint Hint:

Find the length of diameter by distance between two points formula and divide it by 2 to get the legth of radius.

The correct answer is: $2 square root of 2$

If there are two points and ,then distance between two points is

Length of diameter = Distance between (5, 6) and (1, 2)
$d space equals square root of left parenthesis 1 minus 5 right parenthesis squared plus left parenthesis 2 minus 6 right parenthesis squared end root equals square root of left parenthesis negative 4 right parenthesis squared plus left parenthesis negative 4 right parenthesis squared end root equals square root of 16 plus 16 end root equals square root of 32 equals 4 square root of 2$
Length of radius = $1 half$ × Length of diameter
$equals 1 half cross times 4 square root of 2 equals 2 square root of 2$
Therefore, the length of radius of given circle is $2 square root of 2$ .

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