What integer is represented by the phrase"decreased by 4"?
1 answer:
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Answer:
The coordinates of D are (8,3)
Step-by-step explanation:
We have quadrilateral ABCD being a parallelogram with coordinates A(3,2), B(5,4), C(10,5), and D(a,b).
We want to find the coordinates of D.
Since ABCD is a parallelogram, the diagonals AC and BD bisects each other.
The midpoint of AC is (13/2,7/2).
This is also the midpoint of BD.
By the midpoint rule:
This implies that:
Similarly,
The coordinates of D are (8,3)
The given angles are
M = 64
N = 48
where P is unknown. While we don't know P at first, we can solve for it. Recall that for any triangle, the three angles always add to 180 degrees
M+N+P = 180
64+48+P = 180
112+P = 180
112+P-112 = 180-112
P = 68
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So in summary so far
M = 64
N = 48
P = 68
The shortest side is opposite the smallest angle. The side MP is opposite the smallest angle N = 48
The longest side is going to be opposite the largest angle. In this case, side MN is opposite the largest angle P = 68
The medium side is opposite the medium angle. So NP is the medium side length
-------------------------------------------------------
Final Answers:
Shortest Side = MP
Medium Side = NP
Longest Side = MN
See the attached image for a visual summary
The ascending order would be: MP, NP, MN
Note: Something like MP is the same as PM. The order of endpoints for any given individual segment doesn't matter
M = 64
N = 48
where P is unknown. While we don't know P at first, we can solve for it. Recall that for any triangle, the three angles always add to 180 degrees
M+N+P = 180
64+48+P = 180
112+P = 180
112+P-112 = 180-112
P = 68
-------------------------------------------
So in summary so far
M = 64
N = 48
P = 68
The shortest side is opposite the smallest angle. The side MP is opposite the smallest angle N = 48
The longest side is going to be opposite the largest angle. In this case, side MN is opposite the largest angle P = 68
The medium side is opposite the medium angle. So NP is the medium side length
-------------------------------------------------------
Final Answers:
Shortest Side = MP
Medium Side = NP
Longest Side = MN
See the attached image for a visual summary
The ascending order would be: MP, NP, MN
Note: Something like MP is the same as PM. The order of endpoints for any given individual segment doesn't matter