Point H is located at (2,-7). Select all of the following that are 7 units from point H. Choose all answers that apply: A x-axis B (-5,-7) C (-7,7)

Question

Point  H is located at  (2,-7). Select all of the following that are 7 units from point  H. Choose all answers that apply: A  x-axis B  (-5,-7) C  (-7,7)

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Distance Formula Application: To find points that are 7 units away from point H(2,-7), we need to consider the distance formula, which is d = sqrt((x_2 - x_1)^2 + (y_2 - y_1)^2), where d is the distance between two points (x_1, y_1) and (x_2, y_2). We are looking for points where d = 7.Check Option A: Let's first consider option A, the x-axis. The x-axis has the equation y = 0. To find the distance from point H to the x-axis, we only need to consider the y-coordinate of H, which is -7. The distance from H to the x-axis is therefore 7 units, since the x-coordinate does not affect the vertical distance to the x-axis.Check Option B: Now let's check option B, the point (-5,-7). We use the distance formula: d = sqrt((2 - (-5))^2 + (-7 - (-7))^2). Simplifying, we get d = sqrt((2 + 5)^2 + 0^2), which is d = sqrt(7^2). This simplifies to d = 7. So, point (-5,-7) is 7 units away from point H.Check Option C: Finally, let's check option C, the point (-7,7). Again, we use the distance formula: d = sqrt((2 - (-7))^2 + (-7 - 7)^2). Simplifying, we get d = sqrt((2 + 7)^2 + (-7 - 7)^2), which is d = sqrt(9^2 + (-14)^2). This simplifies to d = sqrt(81 + 196), which is d = sqrt(277). The value of sqrt(277) is not 7, so point (-7,7) is not 7 units away from point H.

Point $H$ is located at $(2,-7)$ . Select all of the following that are $7$ units from point $H$ . $\newline$ Choose all answers that apply: $\newline$ A x-axis $\newline$ B $(-5,-7)$ $\newline$ C $(-7,7)$

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Point HHH is located at (2,−7)(2,-7)(2,−7). Select all of the following that are 777 units from point HHH. \newlineChoose all answers that apply:\newlineA x-axis\newlineB (−5,−7)(-5,-7)(−5,−7)\newlineC (−7,7)(-7,7)(−7,7)

Point $H$ is located at $(2,-7)$ . Select all of the following that are $7$ units from point $H$ . $\newline$ Choose all answers that apply: $\newline$ A x-axis $\newline$ B $(-5,-7)$ $\newline$ C $(-7,7)$