Concept explainers
a.
To write: the equations of sides of a rectangle.
a.

Answer to Problem 28PPE
Explanation of Solution
Given information: a figure is given as follows-
The coordinates of corner points of rectangle ABCD are
A(-3, 1), B(3, 3), C(4, 0), D(-2, -2)
Then slope of line AB is
The slope of line BC is
The slope of line CD is
The slope of line DA is
b.
To make: a conjecture about the slopes of the parallel lines.
b.

Explanation of Solution
Given information: a figure is given as follows-
In a rectangle opposite faces are parallel,
And we can also see that in part (a) slopes of parallel faces are equal.
Hence slopes of parallel lines are always equal.
c.
To write: an equation of a line according to the given conditions.
c.

Answer to Problem 28PPE
Explanation of Solution
Given information: a line passes through the point (0, -4) and parallel to the line
a line is given as follows
It is the slope intercept form is and its slope is -7.
The required line is parallel to the given line then its slope will be also -7. And it also passes through (0, -4).
Then its equation is as follows-
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