Directions: Study the given information carefully and answer the question that follows.

Point Q is 12m east of Point P. Point R is 18m north of Point Q. Point S is 8m west of Point R. Point T is 10m south of Point S.

If Point U is 8m north of Point P, then Point T is how far and in which direction from Point U?

The correct answer is 4m, east.

Step-by-step Explanation:

Let us consider Point P as the origin point with coordinates (0, 0), where:
- The positive x-direction represents East and negative x-direction represents West.
- The positive y-direction represents North and negative y-direction represents South.

1. Position of Point Q:
Point Q is 12m east of Point P.
Coordinates of Q = (0 + 12, 0) = (12, 0)

2. Position of Point R:
Point R is 18m north of Point Q.
Coordinates of R = (12, 0 + 18) = (12, 18)

3. Position of Point S:
Point S is 8m west of Point R.
Coordinates of S = (12 - 8, 18) = (4, 18)

4. Position of Point T:
Point T is 10m south of Point S.
Coordinates of T = (4, 18 - 10) = (4, 8)

5. Position of Point U:
Point U is 8m north of Point P.
Coordinates of U = (0, 0 + 8) = (0, 8)

6. Finding distance and direction of Point T from Point U:
Comparing U(0, 8) and T(4, 8):
- Both U and T have the exact same y-coordinate (8m), meaning they lie on the same horizontal line.
- Horizontal distance between U and T:

$\text{Distance}=4-0=4\text{m}$

Since the x-coordinate of T (4) is greater than that of U (0), Point T lies to the East of Point U.

Therefore, Point T is 4m, east from Point U.