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

Full solution

Q. Which of these points are

\sqrt{45}

units away from

(-3,1)

? Select all that apply.

\newline

Multi-select Choices:

\newline

(A)

(3,-2)

\newline

(B)

(-6,-5)

\newline

(C)

(0,7)

\newline

(D)

(-9,4)

Calculate $\sqrt{45}$ : Calculate $\sqrt{45}$ to find the distance we need. $\newline$ $\sqrt{45} \approx 6.708$ (using a calculator).
Check point A: Check each point to see if it's $6.708$ units away from $(-3,1)$ . $\newline$ Start with point A $(3,-2)$ . $\newline$ Distance formula: $\sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}$ $\newline$ Distance from $(-3,1)$ to $(3,-2)$ = $\sqrt{(3 - (-3))^2 + ((-2) - 1)^2}$ = $\sqrt{6^2 + (-3)^2}$ = $\sqrt{36 + 9}$ = $\sqrt{45}$ = $6.708$ .
Check point B: Check point B $(-6,-5)$ . $\newline$ Distance from $(-3,1)$ to $(-6,-5) = \sqrt{(-6 - (-3))^2 + ((-5) - 1)^2} = \sqrt{(-3)^2 + (-6)^2} = \sqrt{9 + 36} = \sqrt{45} = 6.708$ .
Check point C: Check point C $(0,7)$ . $\newline$ Distance from $(-3,1)$ to $(0,7)$ = $\sqrt{(0 - (-3))^2 + (7 - 1)^2}$ = $\sqrt{3^2 + 6^2}$ = $\sqrt{9 + 36}$ = $\sqrt{45}$ = $6.708$ .
Check point D: Check point D $(-9,4)$ . $\newline$ Distance from $(-3,1)$ to $(-9,4) = \sqrt{(-9 - (-3))^2 + (4 - 1)^2} = \sqrt{(-6)^2 + 3^2} = \sqrt{36 + 9} = \sqrt{45} = 6.708$ .