Question

use the diagram to answer the question.
jills house 5 km
6 km
3 km
*not drawn to scale
from her house, jill rode her bike 5 km east, then 6 km south, and then 3 km east.
measured using a single straight line, how far is jill from her house?
a. 5 km
b. 8 km
c. 10 km
d. 14 km

Explanation:

Step1: Calculate total eastward distance

Jill rode 5 km east and then 3 km east. So total eastward distance is \(5 + 3 = 8\) km.

Step2: Identify right triangle legs

The southward distance is 6 km (vertical leg) and eastward distance is 8 km (horizontal leg) of a right triangle.

Step3: Apply Pythagorean theorem

The distance from house is hypotenuse \(c\), where \(a = 6\), \(b = 8\). Using \(c=\sqrt{a^{2}+b^{2}}\), we get \(c=\sqrt{6^{2}+8^{2}}=\sqrt{36 + 64}=\sqrt{100}=10\) km.

Answer:

C. 10 km