## Engage NY Eureka Math 5th Grade Module 6 Lesson 6 Answer Key

### Eureka Math Grade 5 Module 6 Lesson 6 Problem Set Answer Key

Question 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 \(\overline{A B}\) and \(\overline{C D}\).

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 \(\overline{A B}\) that is not at the endpoints, and name it U. Write the coordinates. U ( _____ , _____ )

e. Plot a point on line segment \(\overline{C D}\) and name it V. Write the coordinates. V ( _____ , _____ )

Answer:

a.

b. Line segment \(\overline{C D}\) is parallel to the x-axis and is perpendicular to the y-axis.

c. Line segment \(\overline{A B}\) is parallel to the y-axis and is perpendicular to the x-axis.

d. The coordinates. U ( 0.3 , 0.5 )

e. The coordinates. V ( 0.3 , 0.9 )

Question 2.

Construct line f such that the y-coordinate of every point is 3\(\frac{1}{2}\), and construct line g such that the x-coordinate of every point is 4\(\frac{1}{2}\).

a. Line f is ________ units from the x-axis.

b. Give the coordinates of the point on line f that is \(\frac{1}{2}\) unit from the y-axis. ________

c. With a blue pencil, shade the portion of the grid that is less than 3\(\frac{1}{2}\) 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\(\frac{1}{2}\) units from the y-axis.

Answer:

Line f is drawn with points A and B with the y-coordinate of every point is 3\(\frac{1}{2}\) .

A : (1, 3\(\frac{1}{2}\))

B : (3, 3\(\frac{1}{2}\))

Line g is drawn with points C and D with the x-coordinate of every point is 4\(\frac{1}{2}\) .

C : (4\(\frac{1}{2}\) , 3 )

D : ( 4\(\frac{1}{2}\) , 1)

a. Line f is 4\(\frac{1}{2}\) units from the x-axis.

Explanation :

Distance between f and x-axis is the y-coordinate .

b. The coordinate of the point is ( \(\frac{1}{2}\) , 3\(\frac{1}{2}\) )

c.

d. Line g is 4\(\frac{1}{2}\) units from the y-axis.

Explanation :

Distance between g and y-axis is the x-coordinate .

e. The coordinates of the point on line g that is 5 units from the x-axis is ( 4\(\frac{1}{2}\) , 5 )

f.

Question 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 unit 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 unit and less than 2.4 units from the x-axis.

g. Give the coordinates of a point that lies in the double-shaded region.

Answer:

g. The coordinates of a point that lies in the double-shaded region is (1, 2)

### Eureka Math Grade 5 Module 6 Lesson 6 Exit Ticket Answer Key

Question 1.

Plot the point H (2\(\frac{1}{2}\), 1\(\frac{1}{2}\)).

Answer:

Question 2.

Line l passes through point H and is parallel to the y-axis. Construct line l.

Answer:

Question 3.

Construct line m such that the y-coordinate of every point is \(\frac{3}{4}\).

Answer:

Explanation :

For same y -coordinate of every point is \(\frac{3}{4}\) then draw a line from \(\frac{3}{4}\) from x-axis .

Question 4.

Line m is ________ units from the x-axis.

Answer:

Line m is \(\frac{3}{4}\) units from the x-axis.

Explanation :

It is represented by y-coordinate of line m .

Question 5.

Give the coordinates of the point on line m that is \(\frac{1}{2}\) unit from the y-axis.

Answer:

The coordinates of the point on line m that is \(\frac{1}{2}\) unit from the y-axis is (\(\frac{1}{2}\) , \(\frac{3}{4}\) ).

Question 6.

With a blue pencil, shade the portion of the plane that is less than \(\frac{3}{4}\) unit from the x-axis.

Answer:

Question 7.

With a red pencil, shade the portion of the plane that is less than 2\(\frac{1}{2}\) units from the y-axis.

Answer:

Question 8.

Plot a point that lies in the double-shaded region. Give the coordinates of the point.

Answer:

The point that lies in the double-shaded region is W ( 2 , \(\frac{1}{2}\) )

### Eureka Math Grade 5 Module 6 Lesson 6 Homework Answer Key

Question 1.

Plot and label the following points on the coordinate plane.

C: (0.4, 0.4)

A: (1.1, 0.4)

S: (0.9, 0.5)

T: (0.9, 1.1)

a. Use a straightedge to construct line segments \(\overline{C A}\) and \(\overline{S T}\).

b. Name the line segment that is perpendicular to the x-axis and parallel to the y-axis. _________

c. Name the line segment that is parallel to the x-axis and perpendicular to the y-axis. _________

d. Plot a point on \(\overline{C A}\), and name it E. Plot a point on line segment \(\overline{S T}\), and name it R.

e. Write the coordinates of points E and R.

E ( ____ , ____ ) R ( ____ , ____ )

Answer:

a.

c. The line segment that is perpendicular to the x-axis and parallel to the y-axis is \(\overline{S T}\)

d. The line segment that is parallel to the x-axis and perpendicular to the y-axis is \(\overline{C A}\)

e.

f. The coordinates of points E and R.

E ( 0.8 , 0.4 ) R ( 0.9 , 0.8 )

Question 2.

Construct line m such that the y-coordinate of every point is 1\(\frac{1}{2}\), and construct line n such that the x-coordinate of every point is 5\(\frac{1}{2}\).

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\(\frac{1}{2}\) 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\(\frac{1}{2}\) units from the x-axis.

f. With a red pencil, shade the portion of the grid that is less than 5\(\frac{1}{2}\) units from the y-axis.

Answer:

Line m is drawn with points A and B with the y-coordinate of every point is 1\(\frac{1}{2}\) .

A : (1, 1\(\frac{1}{2}\))

B : (3, 1\(\frac{1}{2}\))

Line n is drawn with points C and D with the x-coordinate of every point is 5\(\frac{1}{2}\) .

C : (5\(\frac{1}{2}\) , 3 )

D : ( 5\(\frac{1}{2}\) , 6)

a. a. Line m is 1\(\frac{1}{2}\) units from the x-axis.

Explanation :

Distance between x-axis and line m is the y coordinate .

b. The coordinates of the point on line m that is 2 units from the y-axis is ( 2, 1\(\frac{1}{2}\) )

c.

d. Line n is 5\(\frac{1}{2}\) units from the y-axis.

Explanation :

Explanation :

Distance between y-axis and line n is the x – coordinate .

e. The coordinates of the point on line n that is 3\(\frac{1}{2}\) units from the x-axis is (5\(\frac{1}{2}\) , 3\(\frac{1}{2}\))

f.

Question 3.

Construct and label lines e, r, s, and o on the plane below.

a. Line e is 3.75 units above the x-axis.

b. Line r is 2.5 units from the y-axis.

c. Line s is parallel to line e but 0.75 farther from the x-axis.

d. Line o is perpendicular to lines s and e and passes through the point (3\(\frac{1}{4}\), 3\(\frac{1}{4}\)).

Answer:

Question 4.

Complete the following tasks on the plane.

a. Using a blue pencil, shade the region that contains points that are more than 2\(\frac{1}{2}\) units and less than 3\(\frac{1}{4}\) units from the y-axis.

b. Using a red pencil, shade the region that contains points that are more than 3\(\frac{3}{4}\) units and less than 4\(\frac{1}{2}\) units from the x-axis.

c. Plot a point that lies in the double-shaded region, and label its coordinates.

Answer:

Explanation :

In double shaded (3,4 ) is a point that is marked as shown in above figure .