 # Interpret Points on the Plane as Distances from the Axes

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Common Core For Grade 5

Examples, videos, and solutions to help grade 5 students learn how to investigate patterns in vertical and horizontal lines, and interpret points on the plane as distances from the axes.

### New York State Common Core Math Grade 5, Module 6, Lesson 6

Lesson 6 Concept Development

Problem 1: Refer to locations as distances from the axes.
Problem 2: Construct horizontal and vertical lines on the coordinate plane.
Problem 3: Identify regions of the plane created by intersecting lines.
Lesson 6 Problem Set

1. Plot the following points, and label them on the coordinate plane.
A: (0.3, 0.1)
B: (0.3, 0.7)
C: (0.2, 0.9)
D: (0.4, 0.9)
a. Use a straightedge to construct line segments AB and CD.
b. Line segment _________ is parallel to the x-axis and is perpendicular to the y-axis.
c. Line segment _________ is parallel to the y-axis and is perpendicular to the x-axis.
d. Plot a point on line segment AB that is not at the endpoints, and name it U.
Write the coordinates. U( _____ , _____ )
e. Plot a point on line segment CD and name it V. Write the coordinates. V( _____ , _____ )

2. Construct line f such that the y-coordinate of every point is 3 1/2, and construct line g such that the x-coordinate of every point is 4 1/2.
a. Line f is ________ units from the x-axis.
b. Give the coordinates of the point on line f that is 1/2 unit from the y-axis. ________
c. With a blue pencil, shade the portion of the grid that is less than 3 1/2 units from the x-axis.
d. Line g is _________ units from the y-axis.
e. Give the coordinates of the point on line g that is 5 units from the x-axis. ________
f. With a red pencil, shade the portion of the grid that is more than 4 1/2 units from the y-axis.

3. Complete the following tasks on the plane below.
a. Construct a line m that is perpendicular to the x-axis and 3.2 units from the y-axis.
b. Construct a line a that is 0.8 units from the x-axis.
c. Construct a line t that is parallel to line m and is halfway between line m and the y-axis.
d. Construct a line h that is perpendicular to line t and passes through the point (1.2, 2.4).
e. Using a blue pencil, shade the region that contains points that are more than 1.6 units and less than 3.2 units from the y-axis.
f. Using a red pencil, shade the region that contains points that are more than 0.8 units and less than 2.4 units from the x-axis.
g. Give the coordinates of a point that lies in the double-shaded region. Lesson 6 Homework

2. Construct line m such that the y-coordinate of every point is 1 1/2 and construct line n such that the x-coordinate of every point is 5 1/2.
a. Line m is ________ units from the x-axis.
b. Give the coordinates of the point on line m that is 2 units from the y-axis. ________
c. With a blue pencil, shade the portion of the grid that is less than 1 1/2 units from the x-axis.
d. Line n is _________ units from the y-axis.
e. Give the coordinates of the point on line n that is 3 1/2 units from the x-axis. ________
f. With a red pencil, shade the portion of the grid that is less than 5 1/2 units from the y-axis.
4. Complete the following tasks on the plane.
a. Using a blue pencil, shade the region that contains points that are more than 2 1/2 units and less than 3 1/4 units from the y-axis.
b. Using a red pencil, shade the region that contains points that are more than 3 3/4 units and less than 4 1/2 units from the x-axis.
c. Plot a point that lies in the double shaded region, and label its coordinates.

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