The equation of the fourth side of the considered parallelogram is y = 2x + 10
Parallel lines have same slope, since slope is like measure of steepness and since parallel lines are of same steepness, thus, are of same slope.
Since given parallel line has equation [tex]y = 2x + 2[/tex], thus its slope is 2 and thus, the slope of the needed line is 2 too.
If the slope of a line is m and the y-intercept is c, then the equation of that straight line is given as:
y = mx + c
To find the slope of a line, we find the rate at which the value of 'y' is increasing as we increase the value of 'x' by one unit.
A parallelogram is a four sided polygon, whose opposite sides are parallel to each other.
The slopes of y = 0 and y = 2 is same. (being 0)
Therefore the fourth side would've same slope as that of y = 2x.
The slope of y = 2x is 2 (the coefficient of x)
Thus, the equation of fourth side would be:
y = 2x + c for some real number c
Let we find the coordinates of four vertices. These are intersections of the equations of the adjacent sides.
Intersection of y = 0:
Putting y = 0 gives 0 = 2x, or x = 0
Thus, the intersection is on (0,0)
Putting y = 0 gives 0 = 2x + c, or x = -c/2
Thus, the intersection is on (-c/2, 0)
Intersection of y = 2:
Putting y = 2 gives 2 = 2x, or x = 1
Thus, the intersection is on (1,2)
Putting y = 2 gives 2 = 2x + c, or x = (2-c)/2
Thus, the intersection is on ((2-c)/2, 2)
Thus, the four vertices' coordinates are:
(0,0), (1,2), (-c/2, 0), and ( (2-c)/2, 0)
Let we name these points, as:
A(0,0), B(-c/2, 0), C( (2-c)/2, 2) and D(1,2),
AB is line y = 0 (known from the y-coordinates of A and B)
Similarly, CD is line y = 2 (known from the y-coordinates of C and D)
AD and BC are parallel. (these are going to be other pair of parallel sides).
The length of AD is:
[tex]\sqrt{(1-0)^2 + (2-0)^2} = \sqrt{5} \: \rm units[/tex]
A parallelogram has its parallel sides of equal length.
Thus, length of BC is of √5 units too.
Since this parallelogram has two side lengths of 5 units, adn as AD and BC are not those sides, so we must have:
|AB| = |CD| = 5 units.
Length of AB is:
[tex]|AB| = \sqrt{(-c/2 - 0)^2 + (0 - 0)^2 } = c/2 = 5\\c = 10[/tex]
Thus, the equation of the fourth line is:
[tex]y = 2x + 10[/tex]
The graph of the considered parallelogram is given below.
Thus, the equation of the fourth side of the considered parallelogram is y = 2x + 10
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