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Sagot :
Answer:
[tex]G = (2,-1)[/tex]
[tex]H = (9,1)[/tex]
Step-by-step explanation:
Given
[tex]E = (4,7)[/tex]
[tex]F=(-3,5)[/tex]
[tex]D =(3,3)[/tex] --- Diagonal
Required
Determine the coordinates of G and H
Since EFGH is a parallelogram, then:
D is the midpoint of EG and EF
For EG, we have:
[tex](3,3) = \frac{1}{2}(4 + x,7+y)[/tex]
Where x, y are the coordinates of G.
Multiply both sides by 2
[tex](6,6) = (4+x,7+y)[/tex]
By comparison:
[tex]4 + x = 6[/tex] ==> [tex]x =2[/tex]
[tex]7 + y= 6[/tex] ==> [tex]y = -1[/tex]
So:
[tex]G = (2,-1)[/tex]
For FH, we have:
[tex](3,3) = \frac{1}{2}(-3 + x,5+y)[/tex]
Where x, y are the coordinates of H.
Multiply both sides by 2
[tex](6,6) = (-3 + x,5+y)[/tex]
By comparison:
[tex]-3+x = 6[/tex] ==> [tex]x = 9[/tex]
[tex]5 + y = 6[/tex] ==> [tex]y =1[/tex]
So:
[tex]H = (9,1)[/tex]
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