NIMCET 2007 — Mathematics PYQ

Step 1: Understand the positions relative to a starting point (Point B)

Let point B be the origin $(0,0)$.

• Point A is 8 miles east of B:

  $$\text{Coordinates of A}=(8,0)$$

• Point C is 10 miles north of B:

  $$\text{Coordinates of C}=(0,10)$$

• Point D is 13 miles east of C:

  $$\text{Coordinates of D}=(0+13,10)=(13,10)$$

• Point E is 2 miles north of D:

  $$\text{Coordinates of E}=(13,10+2)=(13,12)$$

Step 2: Calculate the net horizontal and vertical distance between A and E

• Horizontal distance (East-West difference):

  $$\Delta x=13-8=5\text{ miles}$$

• Vertical distance (North-South difference):

  $$\Delta y=12-0=12\text{ miles}$$

Step 3: Use the Pythagorean Theorem to find the shortest distance (AE)

The shortest distance between A and E forms the hypotenuse of a right-angled triangle with base $5\text{ miles}$ and height $12\text{ miles}$.

$$\text{Shortest Distance (AE)}=\sqrt{(\Delta x{)}^2+(\Delta y{)}^2}$$

$$\text{AE}=\sqrt{5^2+12^2}$$

$$\text{AE}=\sqrt{25+144}$$

$$\text{AE}=\sqrt{169}$$

$$\text{AE}=13\text{ miles}$$

Conclusion

The shortest distance between A and E is 13.

Correct Option: (a) 13