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 (-7, 7) b (-5, -7) c x - axis

Explanation:

Step1: Recall the distance formula or analyze coordinates

For two points \((x_1,y_1)\) and \((x_2,y_2)\), the distance \(d=\sqrt{(x_2 - x_1)^2+(y_2 - y_1)^2}\). But we can also analyze horizontal/vertical distances. Point \(H=(2,-7)\).

Step2: Analyze Option A \((-7,7)\)

Calculate the distance: \(d=\sqrt{(-7 - 2)^2+(7 - (-7))^2}=\sqrt{(-9)^2+(14)^2}=\sqrt{81 + 196}=\sqrt{277}\approx16.64
eq7\). So A is not correct.

Step3: Analyze Option B \((-5,-7)\)

Since the \(y\)-coordinates are the same (\(-7\)), the distance is the absolute difference of \(x\)-coordinates: \(| - 5 - 2|=|-7| = 7\). So B is 7 units from \(H\).

Step4: Analyze Option C (x - axis)

The \(x\)-axis is \(y = 0\). The distance from \((2,-7)\) to \(y = 0\) is the absolute difference of \(y\)-coordinates: \(|0 - (-7)|=|7| = 7\). So the \(x\)-axis is 7 units from \(H\).

Answer:

B. \((-5, -7)\), C. \(x\)-axis