Math Problem Statement

Renee takes a boat directly from the lodge to the campsite. If the distance between grid lines represents 500 feet, how far does Renee travel? Round to the nearest feet. What is the distance between Points E and F? Round to the nearest tenth of a unit. Graph the points (-2, -4) and (-4, -1) and use the grid lines to draw a right triangle with the given points as endpoints of the hypotenuse. Provide a possible coordinate pair for the third vertex. What is the vertical and horizontal distance between the points? What is the distance between the given points? Round to the nearest tenth of a unit. What is the perimeter of the triangle you drew?

Solution

This appears to be a math homework problem involving the application of the Pythagorean Theorem in the coordinate plane.

Let's break down the questions based on the image:

  1. Renee's travel distance:

    • Renee travels a straight line from the lodge to the campsite, with the distance between grid lines representing 500 feet. We need to apply the Pythagorean Theorem to determine how far she travels.
  2. Distance between points E and F:

    • You are asked to find the distance between points E and F, rounded to the nearest tenth of a unit.
  3. Graphing a right triangle:

    • The problem asks you to plot points (-2, -4) and (-4, -1) on your paper and then draw a right triangle using these as endpoints of the hypotenuse. After that, you are to determine:
      • A possible coordinate pair for the third vertex.
      • The vertical and horizontal distances between the points.
      • The distance between these points (rounded to the nearest tenth).
      • The perimeter of the triangle formed by these points.

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Math Problem Analysis

Mathematical Concepts

Pythagorean Theorem
Distance Formula
Coordinate Geometry

Formulas

Pythagorean Theorem: a^2 + b^2 = c^2
Distance Formula: d = sqrt((x2 - x1)^2 + (y2 - y1)^2)

Theorems

Pythagorean Theorem

Suitable Grade Level

Grades 7-9