Exercise 4 Page 357

Two lines are parallel if their slopes are identical. To tell if two lines are perpendicular, we check if a product of their slopes is -1. Let's determine which lines are parallel and which are perpendicular one at a time.

Parallel Lines

For this exercise we have been given two points on each line, so we have enough information to calculate their slopes using the Slope Formula. m=y_2- y_1/x_2- x_1 Note that when choosing points to substitute for ( x_1, y_1) and ( x_2, y_2), it does not matter which points on the line we choose since the result will be the same. Let's start with line a which passes through ( -2, 2) and ( 4, -2).

The slope of line a is - 23. We can use the same method to identify the slopes of lines b, c, and d.

Now that we have identified the slope of each line, we can see that a and b have the same slope which means they are parallel. For lines with different slopes we can conclude that they are not parallel.

Perpendicular Lines

To determine whether or not the lines are perpendicular, we calculate the product of their slopes. Any two lines with the slopes whose product equals -1 are perpendicular. m_1* m_2 ? =-1 Let's start with the slopes - 23 and - 12.

This means that lines a and c as well as b and c, are not perpendicular. We can use a similar method to check if other lines are perpendicular.

We found that lines with slopes of - 12 and 2 are perpendicular. Therefore, c and d are perpendicular.

To sum up, we found that a and b are parallel and c and d are perpendicular.