## Engage NY Eureka Math 5th Grade Module 6 Lesson 3 Answer Key

### Eureka Math Grade 5 Module 6 Lesson 3 Problem Set Answer Key

Question 1.
Use the grid below to complete the following tasks.
a. Construct an x-axis that passes through points A and B.
b. Construct a perpendicular y-axis that passes through points C and F.
c. Label the origin as 0.
d. The x-coordinate of B is 5$$\frac{2}{3}$$. Label the whole numbers along the x-axis.
e. The y-coordinate of C is 5$$\frac{1}{3}$$. Label the whole numbers along the y-axis.  Question 2.
For all of the following problems, consider the points A through N on the previous page.
a. Identify all of the points that have an x-coordinate of 3$$\frac{1}{3}$$.
The points that have an x-coordinate of 3$$\frac{1}{3}$$ are J, I, H and D .

b. Identify all of the points that have a y-coordinate of 2$$\frac{2}{3}$$.
The points that have a y-coordinate of 2$$\frac{2}{3}$$ are E, F, H and K .

c. Which point is 3$$\frac{1}{3}$$ units above the x-axis and 2$$\frac{2}{3}$$ units to the right of the y-axis? Name the point, and give its coordinate pair.
Point H and its coordinate pair is ( 3$$\frac{1}{3}$$ , 2$$\frac{2}{3}$$ )

d. Which point is located 5$$\frac{1}{3}$$ units from the y-axis?
Point C .

e. Which point is located 1$$\frac{2}{3}$$ units along the x-axis?
Point M .

f. Give the coordinate pair for each of the following points.
K: __
I: ______
B: ______
C: ______
The coordinate pair of K is (5$$\frac{1}{3}$$, 2$$\frac{2}{3}$$)
The coordinate pair of I is (3$$\frac{1}{3}$$, 1$$\frac{2}{3}$$)
The coordinate pair of B is (5$$\frac{2}{3}$$, 0)
The coordinate pair of C is (0, 5$$\frac{1}{3}$$ )

g. Name the points located at the following coordinates.
(1$$\frac{2}{3}$$, $$\frac{2}{3}$$) ______
(0, 2$$\frac{2}{3}$$) ______
(1, 0) ______
(2, 5$$\frac{2}{3}$$) ______
h. Which point has an equal x- and y-coordinate? ________
i. Give the coordinates for the intersection of the two axes. (____ , ____) Another name for this point on the plane is the ___________.
j. Plot the following points.
P: (4$$\frac{1}{3}$$, 4)
Q: ($$\frac{1}{3}$$, 6)
R: (4$$\frac{2}{3}$$, 1)
S: (0, 1$$\frac{2}{3}$$)
k. What is the distance between E and H, or EH?
l. What is the length of HD?
m. Would the length of ED be greater or less than EH+HD?
n. Jack was absent when the teacher explained how to describe the location of a point on the coordinate plane. Explain it to him using point J.
(1$$\frac{2}{3}$$, $$\frac{2}{3}$$)  is Point M
(0, 2$$\frac{2}{3}$$) is Point F
(1, 0) is Point  A
(2, 5$$\frac{2}{3}$$) is Point N
h. The point L has an equal x- and y-coordinate
i. (0,0) Origin.
j.
P: (4$$\frac{1}{3}$$, 4)
Q: ($$\frac{1}{3}$$, 6)
R: (4$$\frac{2}{3}$$, 1)
S: (0, 1$$\frac{2}{3}$$) ### Eureka Math Grade 5 Module 6 Lesson 3 Exit Ticket Answer Key

Question 1.
Use a ruler on the grid below to construct the axes for a coordinate plane. The x-axis should intersect points L and M. Construct the y-axis so that it contains points K and L. Label each axis. a. Place a hash mark on each grid line on the x- and y-axis.
b. Label each hash mark so that A is located at (1, 1).
c. Plot the following points:

 Point X -coordinate Y -coordinate B $$\frac{1}{4}$$ 0 C 1 $$\frac{3}{4}$$ ### Eureka Math Grade 5 Module 6 Lesson 3 Homework Answer Key

Question 1.
Use the grid below to complete the following tasks.
a. Construct a y-axis that passes through points Y and Z.
b. Construct a perpendicular x-axis that passes through points Z and X.
c. Label the origin as 0.
d. The y-coordinate of W is 2$$\frac{3}{5}$$. Label the whole numbers along the y-axis.
e. The x-coordinate of V is 2$$\frac{2}{5}$$. Label the whole numbers along the x-axis.  Question 2.
For all of the following problems, consider the points K through X on the previous page.
a. Identify all of the points that have a y-coordinate of 1$$\frac{3}{5}$$.
The points that have a y-coordinate of 1$$\frac{3}{5}$$ are R, M and Q.

b. Identify all of the points that have an x-coordinate of 2$$\frac{1}{5}$$.
The points that have an x-coordinate of 2$$\frac{1}{5}$$ are O, M and L .

c. Which point is 1$$\frac{3}{5}$$ units above the x-axis and 3$$\frac{1}{5}$$ units to the right of the y-axis? Name the point, and give its coordinate pair.
Point P and its coordinate pair is ( 1$$\frac{3}{5}$$ , 3$$\frac{1}{5}$$ )

d. Which point is located 1$$\frac{1}{5}$$ units from the y-axis?
Point K .

e. Which point is located $$\frac{2}{5}$$ unit along the x-axis?
Point R .

f. Give the coordinate pair for each of the following points.
T: ________
U: ________
S: ________
K: ________
The coordinate pair of T is (2$$\frac{3}{5}$$, 2$$\frac{4}{5}$$)
The coordinate pair of U is ( $$\frac{3}{5}$$, $$\frac{3}{5}$$)
The coordinate pair of S is ( 1, $$\frac{2}{5}$$)
The coordinate pair of K is (1$$\frac{1}{5}$$, 3$$\frac{2}{5}$$)

g. Name the points located at the following coordinates.
($$\frac{3}{5}$$, $$\frac{3}{5}$$) ______
(3$$\frac{2}{5}$$, 0) ______
(2$$\frac{1}{5}$$, 3) ______
(0, 2$$\frac{3}{5}$$) ______
($$\frac{3}{5}$$, $$\frac{3}{5}$$) is Point U
(3$$\frac{2}{5}$$, 0) is Point X
(2$$\frac{1}{5}$$, 3) is Point L
(0, 2$$\frac{3}{5}$$) is Point W

h. Plot a point whose x- and y-coordinates are equal. Label your point E.
Point is plotted at (1,1) where x and y coordinates are 1

i. What is the name for the point on the plane where the two axes intersect? ___________ Give the coordinates for this point. ( ____ , ____ )
(0,0) ,Origin .

j. Plot the following points.
A: (1$$\frac{1}{5}$$, 1)
B: ($$\frac{1}{5}$$, 3)
C: (2$$\frac{4}{5}$$, 2$$\frac{2}{5}$$)
D: (1$$\frac{1}{5}$$, 0) k. What is the distance between L and N, or LN?
Point L is at 2$$\frac{1}{5}$$
Point N is at 3
Distance of LN = 3 – 2$$\frac{1}{5}$$ = $$\frac{15}{5}$$ – $$\frac{11}{5}$$= $$\frac{4}{5}$$

l. What is the distance of MQ?
Same y coordinates so subtract only x coordinates .
Point M is at 2$$\frac{1}{5}$$
Point Q is at  3$$\frac{1}{5}$$
Distance of MQ = 3 $$\frac{1}{5}$$ – 2$$\frac{1}{5}$$ = $$\frac{16}{5}$$ – $$\frac{11}{5}[/latex = [latex]\frac{5}{5}$$ =1

m. Would RM be greater than, less than, or equal to LN+MQ?
Point M is at 2$$\frac{1}{5}$$
Point R is at  $$\frac{2}{5}$$
Distance of RM = 2 $$\frac{1}{5}$$ – $$\frac{2}{5}$$ = $$\frac{11}{5}$$ – $$\frac{2}{5}$$ = $$\frac{9}{5}$$
Distance of LN = $$\frac{4}{5}$$
LN +MQ = 1 + $$\frac{4}{5}$$ = $$\frac{9}{5}$$