Study the following information carefully and answer the given question.

Point B is 15m north of point A. Point C is 10m west of point B. Point D is 5m south of point C. Point E is 5m east of point D.

If Point F is 10m west of Point A, then Point D is how far and in which direction from point F?

The correct answer is 10m, north.

Step-by-step Explanation:

Let us map out the locations of all points on a standard two-dimensional coordinate system, where East is along the positive x-axis, West is along the negative x-axis, North is along the positive y-axis, and South is along the negative y-axis.

Let point A be at the origin (0, 0).

1. Point B: Point B is 15m north of Point A.
Coordinates of B = (0, 15)

2. Point C: Point C is 10m west of Point B.
Coordinates of C = (0 - 10, 15) = (-10, 15)

3. Point D: Point D is 5m south of Point C.
Coordinates of D = (-10, 15 - 5) = (-10, 10)

4. Point E: Point E is 5m east of Point D.
Coordinates of E = (-10 + 5, 10) = (-5, 10)

5. Point F: Point F is 10m west of Point A.
Coordinates of F = (0 - 10, 0) = (-10, 0)

Finding the distance and direction of Point D from Point F:

Comparing the coordinates of Point F (-10, 0) and Point D (-10, 10):

• Both points have the same x-coordinate (-10), which means Point D is directly to the North or South of Point F.

• The y-coordinate of Point D (10) is greater than the y-coordinate of Point F (0). Therefore, Point D is in the North direction relative to Point F.

• The distance between Point D and Point F is calculated as:

$\text{Distance}=10-0=10\text{ m}$

Thus, Point D is 10m, north from Point F.