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 $(-7,7)$ c $(-5,-7)$

Explanation:

Step1: Recall distance - related concepts

The distance between two points $(x_1,y_1)$ and $(x_2,y_2)$ is given by $d = \sqrt{(x_2 - x_1)^2+(y_2 - y_1)^2}$. The distance from a point $(x,y)$ to the $x -$axis is $|y|$. Point $H=(2,-7)$.

Step2: Check distance to the $x -$axis

The distance from point $H(2,-7)$ to the $x -$axis is $| - 7|=7$ units.

Step3: Calculate distance to point $(-7,7)$

Let $(x_1,y_1)=(2,-7)$ and $(x_2,y_2)=(-7,7)$. Then $d=\sqrt{(-7 - 2)^2+(7+7)^2}=\sqrt{(-9)^2 + 14^2}=\sqrt{81 + 196}=\sqrt{277}
eq7$.

Step4: Calculate distance to point $(-5,-7)$

Let $(x_1,y_1)=(2,-7)$ and $(x_2,y_2)=(-5,-7)$. Then $d=\sqrt{(-5 - 2)^2+(-7 + 7)^2}=\sqrt{(-7)^2+0^2}=7$.

Answer:

A. $x$-axis, C. $(-5,-7)$