Point A is 30 metres to the east of point B. Point C is 10 metres to the south of Point A. Point D is 15 metres to the west of Point C. Point E is exactly in the middle of the Points D and F. Points D, E and F lie in a straight line. The length of the lin
Point A is 30 metres to the east of point B. Point C is 10 metres to the south of Point A. Point D is 15 metres to the west of Point C. Point E is exactly in the middle of the Points D and F. Points D, E and F lie in a straight line. The length of the line DEF is 20 metres. Point F is to the north of Point D. Point G is 15 metres to the east of Point F. How far and in which direction is Point G from Point A ?
1). 10 metres, South
2). 15 metres. North
3). 10 metres, North
4). 15 metres, South
This Question has 2 answers.
Point A is $30$ meters to the east of Point B.
Point C is $10$ meters to the south of Point A.
Point D is $15$ meters to the west of Point C.
Thus, the coordinates of the points are:
- $ A(30,0) $
- $ C(30,-10) $
- $ D(15,-10) $
Point E is exactly in the middle of Points D and F.
Points D, E, and F lie in a straight line, and the total length of DEF is $20$ meters.
Since Point F is to the north of Point D, we find the coordinates of E and F:
Midpoint of $D$ and $F$:
$ \text{E} = \left( \frac{15 + 15}{2}, \frac{-10 + y}{2} \right) $
Since the total length DEF is $20$ meters, and $E$ is the midpoint, the distance between D and F is $20$ meters.
Thus, $ F $ is $20$ meters north of $D$:
$ F(15,10) $
Point G is $15$ meters to the east of Point F:
$ G(30,10) $
Now, we find the distance and direction of Point G from Point A.
Comparing coordinates:
- $ A(30,0) $
- $ G(30,10) $
Point G is $10$ meters to the north of Point A.
Thus, the correct answer is:
$ \boxed{10 \text{ meters, North}} $
20 m north
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