Question

Point E is located at minus, 14−14. Points F and G are each 6 units away from Point E. Where are F and G located?

Answer 1

Point E is located at \((-14, -14)\). To find points F and G that are each 6 units away from point E, we can use the distance formula, which states that the distance \(d\) between two points \((x_1, y_1)\) and \((x_2, y_2)\) is given by:

\[
d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}
\]

We need to find points F and G such that the distance from E to both points is 6. Thus, we are looking for points \((x, y)\) that satisfy:

\[
\sqrt{(x + 14)^2 + (y + 14)^2} = 6
\]

Squaring both sides, we get:

\[
(x + 14)^2 + (y + 14)^2 = 36
\]

This equation represents a circle centered at point E \((-14, -14)\) with a radius of 6.

To find the coordinates of points F and G, we can move 6 units in different directions from point E. A simple way to do this is to use the angles corresponding to the cardinal directions or also to consider the four quadrants.

1. Moving directly to the right (east):
\[
F_1 = (-14 + 6, -14) = (-8, -14)
\]

2. Moving directly to the left (west):
\[
F_2 = (-14 - 6, -14) = (-20, -14)
\]

3. Moving up (north):
\[
G_1 = (-14, -14 + 6) = (-14, -8)
\]

4. Moving down (south):
\[
G_2 = (-14, -14 - 6) = (-14, -20)
\]

Thus, the points F and G can be any combination of the points found. Thus one possible choice for F could be \((-8, -14)\) and for G could be \((-14, -8)\).

In conclusion, points F and G can be:

1. \((-8, -14)\)
2. \((-20, -14)\)
3. \((-14, -8)\)
4. \((-14, -20)\)

These points represent the options for F and G that are each 6 units away from point E.