To accurately determine the direction of point C with respect to point G, we must carefully trace Kartick's entire car journey, segment by segment, and map out the coordinates of each significant point. For simplicity, let's assume Kartick starts at point A, which we can designate as the origin $\left(0,0\right)$ on a coordinate plane. In this system, positive X-axis represents East, negative X-axis represents West, positive Y-axis represents North, and negative Y-axis represents South.

Kartick's Journey: Step-by-Step Movement Analysis

Let's break down Kartick's travel path to understand the changes in his position:

• From A to B: Kartick drives 30 km towards the South. His X-coordinate remains unchanged, and his Y-coordinate decreases by 30.
• From B to C: From point B, he turns left. Since he was moving South, a left turn means he now moves East for 50 km. His Y-coordinate remains unchanged, and his X-coordinate increases by 50.
• From C to D: At point C, he turns right. As he was moving East, a right turn means he now moves South for 60 km. His X-coordinate remains unchanged, and his Y-coordinate decreases by 60.
• From D to E: From point D, he turns left. Since he was moving South, a left turn means he now moves East for 50 km. His Y-coordinate remains unchanged, and his X-coordinate increases by 50.
• From E to F: At point E, he turns right. As he was moving East, a right turn means he now moves South for 20 km. His X-coordinate remains unchanged, and his Y-coordinate decreases by 20.
• From F to G: From point F, he turns right. Since he was moving South, a right turn means he now moves West for 150 km. His Y-coordinate remains unchanged, and his X-coordinate decreases by 150.
• From G to H: Finally, at point G, he turns right. As he was moving West, a right turn means he now moves North for 80 km and then stops at point H. His X-coordinate remains unchanged, and his Y-coordinate increases by 80.

Positioning Points: Coordinate Mapping of Kartick's Path

Let's map out the coordinates of each important point based on Kartick's movements, assuming A is $\left(0,0\right)$:

Direction of Point C with Respect to Point G

We need to find the direction of Point C $\left(50, -30\right)$ when observed from Point G $\left(-50, -110\right)$. To determine this, we calculate the change in X and Y coordinates from G to C:

• Change in X-coordinate $\left(\Delta X\right)$: We subtract the X-coordinate of G from the X-coordinate of C.
  $\Delta X = X_C - X_G = 50 - \left(-50\right) = 50 + 50 = 100$
• Change in Y-coordinate $\left(\Delta Y\right)$: We subtract the Y-coordinate of G from the Y-coordinate of C.
  $\Delta Y = Y_C - Y_G = -30 - \left(-110\right) = -30 + 110 = 80$

Since the change in the X-coordinate $\left(\Delta X = 100\right)$ is positive, Point C is located to the East of Point G.

Since the change in the Y-coordinate $\left(\Delta Y = 80\right)$ is also positive, Point C is located to the North of Point G.

When a point is both to the North and to the East of a reference point, its direction is said to be North-east.

Final Direction Conclusion

Based on the detailed analysis of Kartick's journey and the calculation of coordinates, Point C is in the North-east direction with respect to Point G.