Multiple choice

What is the area of the circle whose diameter has end points (4, - 2) and (6, - 14)?

  1. 28 π

  2. 32 π

  3. 37 π

  4. 40 π

  5. 48 π
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

The diameter is the distance between (4, -2) and (6, -14). Diameter^2 = (6-4)^2 + (-14 - (-2))^2 = 2^2 + (-12)^2 = 4 + 144 = 148. Radius^2 = Diameter^2 / 4 = 148 / 4 = 37. Area = pi * r^2 = 37 pi.

AI explanation

Using the distance formula, the length of the diameter is the square root of [(6 minus 4) squared plus (negative 14 minus negative 2) squared], which is the square root of (4 plus 144), or the square root of 148. The radius is half of this, so r squared is simply 148 divided by 4, which equals 37. Applying the area of a circle formula, pi times r squared, the area is 37 times pi.

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