Engage NY Eureka Math 5th Grade Module 6 Mid Module Assessment Answer Key

Question 1.
Give the coordinates of each point.

A ________________
B ________________
C ________________
D ________________
E ________________
A ( 3, 4)
B (4, 2)
C ($$\frac{1}{2}$$ , $$\frac{1}{4}$$)
D ( 1, 2$$\frac{1}{2}$$)
E (1$$\frac{3}{4}$$, 4$$\frac{1}{4}$$)
Explanation :
The respective x – coordinate and y- coordinates are written of the given points .

Question 2.
Plot each point in the coordinate plane above, and label each point with F, G, or H.
F (0, 4)
G (2, 1)
H (4$$\frac{3}{4}$$, 3$$\frac{3}{4}$$)

Explanation :
The Given Points F, G and H are marked and is shown in the above graph .

Question 3.
a. Give coordinates for any three points that are on the same vertical line. Include at least one point that has a mixed number as a coordinate.
b. Give coordinates for any three points that are on the same horizontal line. Include at least one point that has a fraction as a coordinate.
a. The 3 points are P ( 3, 2 ), Q ( 3, 3 ) and R (3, 3$$\frac{1}{4}$$)
Explanation :
To form a Vertical line on the graph that mean x-coordinates will be same for all y-coordinates. then a vertical line is formed that is parallel to y-axis .
The points are Marked in the above graph .

b. The 3 points are A ( 1, 2 ), B ( 2$$\frac{1}{2}$$, 2 ) and C (3$$\frac{1}{4}$$, 2)

Explanation :
To form a Horizontal line on the graph that mean y-coordinates will be same for all x-coordinates. then a vertical line is formed that is parallel to x-axis .
The points are Marked in the above graph .

Question 4.
Garrett and Jeffrey are planning a treasure hunt. They decide to place a treasure at a point that is a distance of 5 units from the x-axis and 3 units from the y-axis. Jeffrey places a treasure at point J, and Garrett places one at point G. Who put the treasure in the right place? Explain how you know.

Jeffrey puts the treasure in the right place
Explanation :
The treasure is at at a point that is a distance of 5 units from the x-axis and 3 units from the y-axis at a point ( 5, 3)
Jeffrey marks it correct where as the Garrett marks at a point that is a distance of 3 units from the x-axis and 5 units from the y-axis at a point ( 3, 5)

Question 5.
a. Find the y-coordinates by following the rules given for each table.
Table A: Multiply by $$\frac{1}{2}$$.

 x y 0 1 2 3

Table B: Multiply by $$\frac{1}{4}$$.

 x y 0 1 2 3

b. Graph and label the coordinate pairs from Table A. Connect the points, and label the line a. Graph and label the coordinate pairs from Table B. Connect the points, and label the line b.

c. Describe the relationship between the y-coordinates in Table A and Table B that have the same x-coordinate.
a.
Table A: Multiply by $$\frac{1}{2}$$.
y = $$\frac{1}{2}$$(x) .

 x y 0 0 1 $$\frac{1}{2}$$ 2 1 3 1$$\frac{1}{2}$$

Table B: Multiply by $$\frac{1}{4}$$.
y=$$\frac{1}{4}$$(x)

 x y 0 0 1 $$\frac{1}{4}$$ 2 $$\frac{1}{2}$$ 3 $$\frac{3}{4}$$

Explanation :By following the given rule the y-coordinates are calculated and written in the above tabular columns .
b.

Explanation :
The points of tabular Column A are plotted and written as line a .
The points of tabular Column B are plotted and written as line b
All points are plotted and shown in above graph .
c.
The y coordinates in Tabular Column A are half of the y coordinates in the Tabular Column B

Question 6.
a. Use the graph to give the coordinate pairs of the points marked on the line.

 x y

b. Using this rule, generate three more points that would be on this line but lie beyond the portion of the coordinate plane that is pictured.
______ _______ ________
a.
The coordinate points that are marked on the above graph are .

 x y 1 4 2 6 3 8 4 10 5 12

b.
The Rule used is the y-coordinate is double the x-coordinate and 2 added.
y = 2x + 2
The 3 points that lie on the above line beyond the given line in the above graph are .
x = 6 ; y = 2 (6) + 2 = 12 + 2 = 14 then (6, 14)
x= 8 ; y = 2 (8) + 2 = 16 + 2 = 18 then (8, 18)
x= 10; y = 2(10) + 2 = 20 + 2 = 22 then (10, 22 )
(6, 14), (8, 18) and (10, 22 ) are 3 points .

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