Question

A car starts from an office building, which is 5 miles east and 2 miles south of the town center. The car travels 6 miles north, makes a left turn and then travels 8 miles. What is the car’s final position? What single translation vector moves the car from its starting position to its final position?

Answer 1

`\displaystyle \binom{-8}{6}`

Explanation:

The car's starting position is 2 miles south of the town center. If it travels 6 miles north, then it will be 4 miles north of the town center.

The car's starting position is 5 miles east of the town center. If it travels 8 miles west, it will be 3 miles west of the town center.

Therefore, its final position is 4 miles north and 3 miles west of the town center.

If the car travels 6 miles north from it's starting position, the y-value of the vector will be 6, as the car is moving in a positive direction along the y-axis.

If the car travels 8 miles left, the x-value of the vector will be -8, as the car is moving in a negative direction along the x-axis.

Therefore, the single translation vector that moves the car from its starting position to its final position is:

`\displaystyle \binom{x}{y}=\binom{-8}{6}`