Question

What is the radius of the circle?
(-5,12)

Answer 1

Answer: 13

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Step-by-step explanation:

I'm assuming the center of this circle is the origin (0,0)

The distance from the center to any point on the circle's edge is the radius.

So we need to find the distance from (0,0) to (-5,12).

Use the distance formula.

`(x_1,y_1) = (0,0) \text{ and } (x_2, y_2) = (-5,12)\\\\d = √((x_1 - x_2)^2 + (y_1 - y_2)^2)\\\\d = √((0-(-5))^2 + (0-12)^2)\\\\d = √((0+5)^2 + (0-12)^2)\\\\d = √((5)^2 + (-12)^2)\\\\d = √(25 + 144)\\\\d = √(169)\\\\d = 13\\\\`

The distance from (0,0) to (-5,12) is 13 units, which is the radius of this circle.

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Another approach:

Draw a vertical line from (-5,12) down to the x axis. Also connect (-5,12) to the origin (0,0).

This forms a right triangle with legs of a = 5 and b = 12.

Use the pythagorean theorem to find the hypotenuse c.

`a^2 + b^2 = c^2\\\\5^2 + 12^2 = c^2\\\\25 + 144 = c^2\\\\169 = c^2\\\\c^2 = 169\\\\c = √(169)\\\\c = 13\\\\`

The hypotenuse is 13 units which is the radius of this circle.

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The distance formula is a modified version of the pythagorean theorem.

This is because
`a^2 + b^2 = c^2` can be solved to
`c = √(a^2+b^2)\\\\`

• a = horizontal leg = horizontal distance between the two points
• b = vertical leg = vertical distance between the two points

In other words,

`a = |x_1-x_2|\\\\b = |y_1-y_2|\\\\`