Question

A mountain's approximate shape is modeled on the coordinate plane below, with each unit on the plane representing 1,000 feet.

The graph with a scale drawing of a triangle ABC is having horizontal distance on x-axis and height on y-axis, both in increments of 2. Point A is at (1, 0), Point B is at (3, 5) and Point C is at (7, 0).

Enter the distance from point A at the bottom of the mountain to point B at the top of the mountain. Round your answer to the nearest foot.
​
feet

Answer 1

To find the distance from point A to point B, we can use the distance formula, which is given by:

\[
d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}
\]

Here, we have the coordinates of points A and B:
- Point A: \( (1, 0) \)
- Point B: \( (3, 5) \)

Now, substituting the coordinates into the distance formula:

\[
d = \sqrt{(3 - 1)^2 + (5 - 0)^2}
\]

Calculating the differences:

\[
d = \sqrt{(2)^2 + (5)^2}
\]
\[
d = \sqrt{4 + 25}
\]
\[
d = \sqrt{29}
\]

Now, we calculate \(\sqrt{29}\):

\(\sqrt{29} \approx 5.385\)

Since each unit on the graph represents 1,000 feet, we need to multiply the distance by 1,000 to convert it to feet:

\[
5.385 \times 1000 \approx 5385 \text{ feet}
\]

Rounding to the nearest foot gives us:

\[
\boxed{5385} \text{ feet}
\]