Given:
In parallelogram ABCD, two of its vertices are A(-4,0) and B(0,3).
To find:
The equation that represents a line that contain CD.
Solution:
We have,
A(-4,0) and B(0,3)
Slope of AB is
[tex]m=\dfrac{y_2-y_1}{x_2-x_1}[/tex]
[tex]m=\dfrac{3-0}{0-(-4)}[/tex]
[tex]m=\dfrac{3}{4}[/tex]
The slope of line AB is [tex]\dfrac{3}{4}[/tex].
Opposite sides of a parallelogram are parallel and slopes of parallel lines are equal.
In parallelogram ABCD, AB and CD are opposite sides. So, their slopes must be equal.
Slope of line AB = Slope of line CD = [tex]\dfrac{3}{4}[/tex]
The slope intercept form of a line is
[tex]y=mx+b[/tex]
Where, m is slope and b is y-intercept.
Slope of line CD is [tex]\dfrac{3}{4}[/tex], it means the line must be of the form
[tex]y=\dfrac{3}{4}x+b[/tex]
Coefficient of x is [tex]\dfrac{3}{4}[/tex] only in option a.
Therefore, the correct option is a.
