Question

1. ben lives at the origin. ali lives 6 km north of ben. ben lives 10 km east of derek. derek lives east of ben. a. make a sketch to show this information. (2 marks) b. find the shortest distance from ali to derek. (2 marks) a² + b² = c² 10²+6² = c² 10² + 6² = 136 11.6 km + 1/2 3 sig fig

Explanation:

Step1: Identify right - triangle sides

Ben is at the origin. Derek is 10 km east of Ben and Ali is 6 km north of Ben. The horizontal distance between Ali and Derek is 10 km and the vertical distance is 6 km. These form the two legs of a right - triangle.

Step2: Apply Pythagorean theorem

The Pythagorean theorem is $a^{2}+b^{2}=c^{2}$, where $a = 10$ km and $b = 6$ km. Substitute the values: $c=\sqrt{10^{2}+6^{2}}=\sqrt{100 + 36}=\sqrt{136}\approx11.66$ km.

Answer:

$11.7$ km (rounded to 3 significant figures)