Question

If Alberto's school is 3 miles due south of his house and 4 miles due west of Jimmy's house, what is the straight line distance between Alberto's house and Jimmy's house?
Responses
A 3 miles3 miles
B 4 miles4 miles
C 5 miles5 miles
D 6 miles6 miles
E 7 miles

Answer 1

To find the straight line distance between Alberto's house and Jimmy's house, we can represent their locations on a coordinate system.

Let's assign the following coordinates:
- Let Alberto's house be at point \( A(0, 0) \).
- Since the school is 3 miles due south of Alberto's house, it is at point \( S(0, -3) \).
- The school is also 4 miles due west of Jimmy's house, placing Jimmy's house at point \( J(-4, -3) \).

Now we need to find the distance between points \( A(0, 0) \) and \( J(-4, -3) \).

We can use the distance formula:
\[
d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}
\]
In our case, \( (x_1, y_1) = (0, 0) \) and \( (x_2, y_2) = (-4, -3) \). Plugging in these coordinates:

\[
d = \sqrt{((-4) - 0)^2 + ((-3) - 0)^2}
\]
\[
d = \sqrt{(-4)^2 + (-3)^2}
\]
\[
d = \sqrt{16 + 9}
\]
\[
d = \sqrt{25}
\]
\[
d = 5
\]

Thus, the straight line distance between Alberto's house and Jimmy's house is **5 miles**. The correct response is:

C 5 miles