Searching a Region in the Plane

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New York State Common Core Math Geometry, Module 4, Lesson 1

Worksheets for Geometry

Student Outcomes

Given a physical situation (e.g., a room of a certain shape and dimensions, with objects at certain positions and a robot moving across the room), students impose a coordinate system and describe the given in terms of polygonal regions, line segments, and points in the coordinate system.

Searching a Region in the Plane


Exploratory Challenge

Students in a robotics class must program a robot to move about an empty rectangular warehouse. The program specifies location at a given time 𝑡 seconds. The room is twice as long as it is wide. Locations are represented as points in a coordinate plane with the southwest corner of the room deemed the origin, (0,0), and the northeast corner deemed the point (2000,1000) in feet, as shown in the diagram below.

The first program written has the robot moving at a constant speed in a straight line. At time 𝑡 = 1 second, the robot is at position (30,45), and at 𝑡 = 3 seconds, it is at position (50,75). Complete the exercises, and answer the questions below to program the robot’s motion.
a. At what location will the robot hit the wall?
b. At what speed will the robot hit the wall?
c. At what time will the robot hit the wall?


  1. Plot the points on a coordinate plane.
  2. Draw the segment connecting the points.
  3. How much did the 𝑥-coordinate change in 2 seconds?
  4. How much did the 𝑦-coordinate change in 2 seconds?
  5. What is the ratio of change in 𝑦 to the change in 𝑥?
  6. What is the equation of the line of motion?
  7. What theorem could be used to find the distance between the points?
  8. How far did the robot travel in 2 seconds?

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