Question

One line passes through the points (-8,1) and (4,4). Another line passes through points (-9,-7) and (9,-3). Are the lines parallel, perpendicular, or neither?

O Parallel
O Perpendicular
O Neither

Answer 1

The lines passing through (-8,1) and (4,4) and through (-9,-7) and (9,-3) are neither parallel nor perpendicular to each other, as their slopes are 1/4 and 2/9 respectively, and these do not satisfy the conditions for parallel or perpendicular lines. The correct answer is neither.

Step-by-step explanation:

To determine if two lines are parallel, perpendicular, or neither, we must first calculate the slope of each line. The slope is the ratio of the change in the y-value to the change in the x-value between two points on a line (rise over run).

For the first line, which passes through the points (-8,1) and (4,4), the slope (m1) is calculated as follows:

1. Change in y: 4 - 1 = 3
2. Change in x: 4 - (-8) = 12
3. m1 = 3 / 12 = 1 / 4

For the second line, which passes through the points (-9,-7) and (9,-3), the slope (m2) is calculated as follows:

1. Change in y: -3 - (-7) = 4
2. Change in x: 9 - (-9) = 18
3. m2 = 4 / 18 = 2 / 9

Now that we have both slopes, we can compare them. Lines are parallel if they have the same slope and perpendicular if the product of their slopes is -1. In this case, since 1/4 is not equal to 2/9, and the product (1/4) * (2/9) is not equal to -1, the lines are neither parallel nor perpendicular to each other.

The correct option is: Neither.