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On a coordinate plane, a circle has a center at (negative 2, 0). Point (negative 2, 4) lies on the circle.

Distance formula: StartRoot (x 2 minus x 1) squared + (y 2 minus y 1) squared EndRoot


Does the point (1, StartRoot 7 EndRoot) lie on the circle shown?

Explain.


Yes, the distance from (–2, 4) to (–2, 0) is 4 units.

Yes, the distance from (–2, 0) to (1, StartRoot 7 EndRoot) is 4 units.

No, the distance from (–2, 0) to (1, StartRoot 7 EndRoot) is not 4 units.

No, the distance from (–2, 4) to (1, StartRoot 7 EndRoot) is not 4 units.

Respuesta :

Answer:

its the second option

Step-by-step explanation:

i just took the test

Lanuel

Based on the calculations, we can deduce that: B. yes, the distance from (–2, 0) to (1, √7) is 4 units.

Given the following data:

  • Point (x, y) = (-2, 4).
  • Center (h, k) = (-2, 0).

The equation of a circle.

Mathematically, the standard form of the equation of a circle is given by;

(x - h)² +(y - k)² = r²

Where:

  • h and k represents the coordinates at the center.
  • r is the radius of a circle.

Note: The radius of a circle on a coordinate plane is equal to the distance between the center and the point (-2, 4), which is 4 units.

Substituting the given points into the formula, we have;

(x - (-2))² +(y - 0)² = 4²

(x + 2)² +(y - 0)² = 16

How to determine if the point lie on the circle?

We would determine the distance (D) between point (-2, 0) and (1, √7) by using the distance formula for coordinates:

D = √[(x₂ - x₁)² + (y₂ - y₁)²]

D = √[(1 - (-2))² + (√7 - 0)²]

D = √[3² + (√7)²]

D = √9 + 7

D = √16

D = 4 units.

Therefore, the point lie on the circle because the radius of the circle is equal to the distance between the center and the given point.

Read more on coordinate plane here: https://brainly.com/question/15032390

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