Question

Tell whether the lines through the given points are parallel, perpendicular, or neither.

1. (10,5), (-8, 9)
2.(2, - 4), (11, - 6)

Answer 1

By calculating slopes and comparing them, we determined that the lines through the points (10,5) and (-8, 9) and the points (2, -4) and (11, -6) have the same slope of -2/9, which means they are parallel to each other.

Step-by-step explanation:

To determine whether the lines through the given points are parallel, perpendicular, or neither, we calculate the slopes of the lines and compare them. Two lines are parallel if their slopes are equal. They are perpendicular if the product of their slopes is -1.

For the first pair of points (10,5) and (-8, 9), the slope can be found using the formula:

m = (y2 - y1)/(x2 - x1)

Substituting the values, we get:

m1 = (9 - 5)/(-8 - 10) = 4 / -18 = -2/9

For the second pair of points (2, -4) and (11, -6), we do the same:

m2 = (-6 + 4)/(11 - 2) = -2 / 9

Since the slopes m1 and m2 are equal and are not zero, the lines are parallel but not horizontal.