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: Calculate distance to x - axis

The y - coordinate of point H is - 7. The distance from point H(2, - 7) to the x - axis (where y = 0) is |-7 - 0|=7 units.

Step2: Calculate distance to point (-7, 7)

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

Step3: Calculate distance to point (-5, -7)

Use the distance formula. Here, $(x_1,y_1)=(2,-7)$ 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. $(-5,-7)$