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Which of the following points has a distance of 10 from the point (-1,2)?

A.(-11.2)
B.(-1,10)
C.(-1,-12)
D.(10,2)

3 answers

To determine which of the given points has a distance of 10 from the point (-1, 2), we can use the distance formula. The distance between two points \((x_1, y_1)\) and \((x_2, y_2)\) is given by:

\[ d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2} \]

In our case, \((x_1, y_1) = (-1, 2)\) and we want to check each of the provided points.

  1. Point A: (-1, 2) \[ d = \sqrt{((-1) - (-1))^2 + (2 - 2)^2} = \sqrt{0^2 + 0^2} = \sqrt{0} = 0 \quad \text{(not at distance 10)} \]

  2. Point B: (-1, 10) \[ d = \sqrt{((-1) - (-1))^2 + (10 - 2)^2} = \sqrt{0^2 + 8^2} = \sqrt{64} = 8 \quad \text{(not at distance 10)} \]

  3. Point C: (-1, -12) \[ d = \sqrt{((-1) - (-1))^2 + (-12 - 2)^2} = \sqrt{0^2 + (-14)^2} = \sqrt{196} = 14 \quad \text{(not at distance 10)} \]

  4. Point D: (10, 2) \[ d = \sqrt{(10 - (-1))^2 + (2 - 2)^2} = \sqrt{(11)^2 + 0^2} = \sqrt{121} = 11 \quad \text{(not at distance 10)} \]

None of the options A, B, C, or D is at a distance of 10 from the point (-1, 2). Please check if there are other points you would like to evaluate.

choose one

I apologize for the misunderstanding in my previous response. Let's reevaluate the options clearly to find the point that is at a distance of 10 from (-1, 2) using the distance formula.

We can set up the equation for each point \((x, y)\) as follows:

\[ d = \sqrt{(x + 1)^2 + (y - 2)^2} = 10 \]

Squaring both sides:

\[ (x + 1)^2 + (y - 2)^2 = 100 \]

Now let's check the options:

  1. Point A: (-11, 2) \[ d = \sqrt{((-11) + 1)^2 + (2 - 2)^2} = \sqrt{(-10)^2 + 0^2} = \sqrt{100} = 10 \quad \text{(valid)} \]

  2. Point B: (-1, 10) \[ d = \sqrt{((-1) + 1)^2 + (10 - 2)^2} = \sqrt{0^2 + 8^2} = \sqrt{64} = 8 \quad \text{(not valid)} \]

  3. Point C: (-1, -12) \[ d = \sqrt{((-1) + 1)^2 + (-12 - 2)^2} = \sqrt{0^2 + (-14)^2} = \sqrt{196} = 14 \quad \text{(not valid)} \]

  4. Point D: (10, 2) \[ d = \sqrt{(10 + 1)^2 + (2 - 2)^2} = \sqrt{(11)^2 + 0^2} = \sqrt{121} = 11 \quad \text{(not valid)} \]

From this analysis, the only point that is at a distance of 10 from (-1, 2) is:

Point A: (-11, 2).