Question:
Solution:
According to the figure, we have that:
[tex]JH\text{ = GH-GJ}[/tex]
that is:
[tex]JH\text{ = (10x+2)-(7x-5)}[/tex]
this is equivalent to:
[tex]JH\text{ = 3x +7}[/tex]
now, the diagonals of a parallelogram bisect each other. So that, we get the following equation:
[tex]GJ=JH[/tex]
this is equivalent to:
[tex]7x-5=3x+7[/tex]
this is equivalent to:
[tex]7x-3x\text{ = 7+5}[/tex]
this is equivalent to:
[tex]4x\text{ = 12}[/tex]
solving for x, we get:
[tex]x\text{ = }\frac{12}{4}\text{ = 3}[/tex]
On the other hand, remember again that the diagonals of a parallelogram bisect each other. So that, we get the following equation:
[tex]EJ=JI[/tex]
this is equivalent that
[tex]37-2y=4y-5[/tex]
this is equivalent to:
[tex]4y\text{ +2y = 37+5}[/tex]
this is equivalent to:
[tex]6y\text{ = 42}[/tex]
solving for y, we get:
[tex]y\text{ = }\frac{42}{6}\text{ = 7}[/tex]
now, applying the values obtained for x and y we get:
[tex]GJ\text{ = 7x -5 = 7(3)-5 = 16}[/tex]
and
[tex]IJ\text{ = 4y-5 = 4(7)-5 = 23}[/tex]
we can conclude that the correct answer is:
[tex]x\text{ = 3}[/tex]
[tex]y\text{ = 7}[/tex]
[tex]GJ\text{ = 16}[/tex]
[tex]IJ\text{ = 23}[/tex]
