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Zorluk: KolayDistance and Midpoint Formulas

A circle in the standard (x,y)(x, y) coordinate plane has its center at (2,−1)(2, -1) and passes through the point (5,3)(5, 3). What is the diameter, in coordinate units, of the circle?

  1. A
    5
  2. 10Cevap
  3. C
    14
  4. D
    25
  5. E
    50

Cevap

10
The distance between the center of the circle at (2,−1)(2, -1) and the point on the circle (5,3)(5, 3) represents the radius (rr). Applying the distance formula: r=(5−2)2+(3−(−1))2=32+42=25=5r = \sqrt{(5 - 2)^2 + (3 - (-1))^2} = \sqrt{3^2 + 4^2} = \sqrt{25} = 5. Since the diameter of a circle is twice its radius, the diameter is 2×5=102 \times 5 = 10.

Adım Adım Çözüm

1
Use the distance formula to find the radius of the circle, which is the distance between the center (2,−1)(2, -1) and the point (5,3)(5, 3).
r=(5−2)2+(3−(−1))2=32+42=9+16=25=5r = \sqrt{(5 - 2)^2 + (3 - (-1))^2} = \sqrt{3^2 + 4^2} = \sqrt{9 + 16} = \sqrt{25} = 5
The radius of a circle is the distance between its center and any point on its boundary.
2
Multiply the radius by 2 to find the diameter of the circle.
d=2r=2(5)=10d = 2r = 2(5) = 10
The diameter of a circle is always twice the length of its radius.

Anahtar Kavram

Calculating the radius of a circle using the distance formula and doubling it to find the diameter.
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Konular

Distance and Midpoint Formulas

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