Which of these points are sqrt 45 units away from (-3,1)? Select all that apply. Multi-select Choices: (A)(-6,-5) (B)(0,7) (C)(3,-2) (D)(-9,4)

Calculate Distance Formula: Calculate the distance from each point to (-3,1) using the distance formula: Distance = sqrt((x2 - x1)^2 + (y2 - y1)^2), where (x1, y1) = (-3,1) and (x2, y2) are the coordinates of each point given. Point A Calculation: For point A (-6,-5): Distance = sqrt((-6 + 3)^2 + (-5 - 1)^2) = sqrt((-3)^2 + (-6)^2) = sqrt(9 + 36) = sqrt(45). Point B Calculation: For point B (0,7): Distance = sqrt((0 + 3)^2 + (7 - 1)^2) = sqrt(3^2 + 6^2) = sqrt(9 + 36) = sqrt(45). Point C Calculation: For point C (3,-2): Distance = sqrt((3 + 3)^2 + (-2 - 1)^2) = sqrt(6^2 + (-3)^2) = sqrt(36 + 9) = sqrt(45). Point D Calculation: For point D (-9,4): Distance = sqrt((-9 + 3)^2 + (4 - 1)^2) = sqrt((-6)^2 + 3^2) = sqrt(36 + 9) = sqrt(45).

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Math Problems

Grade 7

Estimate square roots

Full solution

Q. Which of these points are

\sqrt{45}

units away from

(-3,1)

? Select all that apply.

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Multi-select Choices:

\newline

(A)

(-6,-5)

\newline

(B)

(0,7)

\newline

(C)

(3,-2)

\newline

(D)

(-9,4)

Calculate Distance Formula: Calculate the distance from each point to $(-3,1)$ using the distance formula: $\text{Distance} = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}$ , where $(x_1, y_1) = (-3,1)$ and $(x_2, y_2)$ are the coordinates of each point given.
Point A Calculation: For point A $(-6,-5)$ : Distance = $\sqrt{(-6 + 3)^2 + (-5 - 1)^2} = \sqrt{(-3)^2 + (-6)^2} = \sqrt{9 + 36} = \sqrt{45}$ .
Point B Calculation: For point B $(0,7)$ : Distance $= \sqrt{(0 + 3)^2 + (7 - 1)^2} = \sqrt{3^2 + 6^2} = \sqrt{9 + 36} = \sqrt{45}$ .
Point C Calculation: For point C $(3,-2)$ : Distance $= \sqrt{(3 + 3)^2 + (-2 - 1)^2} = \sqrt{6^2 + (-3)^2} = \sqrt{36 + 9} = \sqrt{45}$ .
Point D Calculation: For point D $(-9,4)$ : Distance = $\sqrt{(-9 + 3)^2 + (4 - 1)^2} = \sqrt{(-6)^2 + 3^2} = \sqrt{36 + 9} = \sqrt{45}$ .