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8_murik_8 [283]
3 years ago
8

Which point does not lie on the circle centered at (3, 2) with radius 5? A) (0, 6) B) (3, -3) C) (-2, 2) D) (3, 0)

Mathematics
1 answer:
vladimir1956 [14]3 years ago
7 0

Answer:

D

Step-by-step explanation:

The equation of a circle in standard form is

(x - h)² + (y - k)² = r²

where (h, k) are the coordinates of the centre and r is the radius

here (h, k) = (3, 2) and r = 5, hence

(x - 3)² + (y - 2)² = 25 ← equation of circle

If an ordered pair lies on the circle then it satisfies the equation, if not then it does not lie on the circle.

Substitute the coordinates of the points into the left side of the equation of the circle and check validity.

A

(0 , 6) : (0 - 3)² + (6 - 2)² = 9 + 16 = 25 ← lies on circle

B

(3, - 3) : (3 - 3)² + (- 3 - 2)² = 0 + 25 = 25 ← lies on circle

C

(- 2, 2) : (- 2 - 3)² + (2 - 2)² = 25 + 0 = 25 ← lies on circle

D

(3, 0) : (3 - 3)² + (0 - 2)² = 0 + 4 = 4 ≠ 25 ← not on circle

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Step-by-step explanation:

As long as you're seeking outside help, the use of a suitable tool is appropriate. Many graphing calculators, apps, and web sites are available for solving triangles.

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<em>Comment on triangle solutions</em>

These are straightforward because you're given two angles. If you're given two sides and an angle, the solution method varies depending on which angle you're given (opposite the long side, the short side, or the unknown side). In the last case, the law of cosines is involved. In the second case, there are likely two solutions. Once you have two angles, you can proceed as above.

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