Problem Solving on the Coordinate Plane

Videos and solutions to help Grade 6 students learn how solve problems related to the distance between points that lie on the same horizontal or vertical line and the coordinate plane.

New York State Common Core Math Grade 6, Module 3, Lesson 19

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New York State Common Core Math Module 3, Grade 6, Lessons 19

Worksheets for Grade 6

Lesson 19 Student Outcomes

Students solve problems related to the distance between points that lie on the same horizontal or vertical line.

Students use the coordinate plane to graph points, line segments and geometric shapes in the various quadrants and then use the absolute value to find the related distances.

Opening Exercise

In the coordinate plane, find the distance between the points using absolute value.

Exercises

1. Locate and label (4, 5) and 4, –3 ) Draw the line segment between the endpoints given on the coordinate plane. How long is the line segment that you drew? Explain.

2. Draw a horizontal line segment starting at (4, -3) that has a length of units. What are the possible coordinates of the other endpoint of the line segment? (There is more than one answer.)

Which point do you choose to be the other endpoint of the horizontal line segment? Explain how and why you chose that point. Locate and label the point on the coordinate grid.

3. The two line segments that you have just drawn could be seen as two sides of a rectangle. Given this, the endpoints of the two line segments would be three of the vertices of this rectangle.
a. Find the coordinates of the fourth vertex of the rectangle. Explain how you find the coordinates of the fourth vertex using absolute value.
b. How does the fourth vertex that you found relate to each of the consecutive vertices in either direction? Explain.
c. Draw the remaining sides of the rectangle.

4. Using the vertices that you have found and the lengths of the line segments between them, find the perimeter of the rectangle.

5. Find the area of the rectangle.

6. Draw a diagonal line segment through the rectangle with opposite vertices for endpoints. What geometric figures are formed by this line segment? What are the areas of each of these figures? Explain.

7. Construct a rectangle on the coordinate plane that satisfies each of the criteria listed below. Identify the coordinate of each of its vertices.

• Each of the vertices lies in a different quadrant.
• Its sides are either vertical or horizontal.
• The perimeter of the rectangle is 28 units.

Using absolute value, show how the lengths of the sides of your rectangle provide a perimeter of 28 units.

Lesson Summary

The length of a line segment on the coordinate plane can be determined by finding the distance between its endpoints.

You can find the perimeter and area of figures such as rectangles and right triangles by finding the lengths of the line segments that make up their sides, and then using the appropriate formula.

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Lesson 19 Classwork

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Lesson 19 Problem Set

1. One endpoint of a line segment is (-3, -6). The length of the line segment is 7 units. Find four points that could serve as the other endpoint of the given line segment.

2. Two of the vertices of a rectangle are (1, -6) and (-8, -6). If the rectangle has a perimeter of 26 units, what are the coordinates of its other two vertices?

3. A rectangle has a perimeter of 28 units, an area of 48 square units, and sides that are either horizontal or vertical. If one vertex is the point (-5,-7) and the origin is in the interior of the rectangle, find the vertex of the rectangle that is opposite (-5,-7).

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