Exercise 16 Page 181

Two lines are parallel if their slopes are identical. To tell if two lines are perpendicular, we check if their slopes are negative reciprocals. Let's tackle these one at a time.

Are They Parallel?

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 you choose, since the result will be the same. Let's start with line a, which passes through ( 2, 10) and ( 4, 13).

We will use a similar method to identify the slopes of lines b and c.

Now that we have identified the slope of each line, we can see that a and b have the same slope, so they are parallel.

Are They Perpendicular?

For lines with different slopes, we can conclude that they are not parallel. To determine whether or not they are perpendicular, we calculate the product of their slopes. Any two slopes whose product equals -1 are negative reciprocals, and therefore perpendicular. Let's start with checking lines a and c.

Therefore, lines a and c are neither parallel nor perpendicular. We will use a similar method to check if lines a and b or b and c are perpendicular.

None of the products is equal to -1, so none of the lines are perpendicular. Notice that when two lines are parallel, they cannot also be perpendicular.