Question

You are setting up a zip line in your yard. You map out your yard in a coordinate plane. An equation of the line representing the zip line is y = -3/8x + 8. There is a tree in your yard at the point (3,16). Each unit in the coordinate plane represents 1 foot. Approximately how far away is the tree from the zip line? Round your answer to the nearest tenth.

Options:
Option 1: 0.4 feet
Option 2: 2.1 feet
Option 3: 3.2 feet
Option 4: 4.8 feet

Answer 1

The distance between the tree and the zip line is approximately 3.2 feet.

Step-by-step explanation:

To find the distance between the tree and the zip line, we need to find the perpendicular distance from the point (3, 16) to the line y = -3/8x + 8. This can be done using the formula for the distance between a point and a line.

The formula for the distance between a point (x₁, y₁) and a line Ax + By + C = 0 is given by:

distance = |Ax₁ + By₁ + C| / √(A² + B²)

For the equation y = -3/8x + 8, we have A = 3/8, B = 1, and C = -8. Plugging in the values for the coordinates of the tree, we get:

distance = |(3/8)(3) + (1)(16) - (-8)| / √((3/8)² + 1²)

Calculating this expression gives us a distance of approximately 3.2 feet.