The figure created by the intersection of streets is a rectangle.
Procedure - Classification of a quadrilateral based on the functions representing streets
Now we proceed to transform each linear function into its explicit form:
Oak street
[tex]y = -3\cdot x + 5[/tex] (1)
Palm street
[tex]y = \frac{1}{3}\cdot x - 2[/tex] (2)
Bird street
[tex]y = -3\cdot x -4[/tex] (3)
Deer street
[tex]y = \frac{1}{3}\cdot x + 1[/tex] (4)
Analysis of the quadrilateral
From analytic geometry we know the following facts:
- Two lines are parallel when both have the same slope but distinct intercepts.
- Two lines are perpendicular when they observe the following relationship: [tex]m_{1}\cdot m_{2} = -1[/tex].
By geometry we also know the following facts:
- A rectangle has two pairs of opposite parallel lines and four pairs of neighboring perpendicular lines.
- A parallelogram has only two pairs of opposite parallel lines.
- A trapezoid has only a pair of opposite parallel lines.
According to all this information, we conclude that the figure created by the intersection of streets is a rectangle. [tex]\blacksquare[/tex]
To learn more on rectangles, we kindly invite to check this verified question: https://brainly.com/question/10046743
