Question

Given P(-2, 2), Q(2, 1), R(1, -1), and S(5, -2), determine if lines PQ and RS are parallel, perpendicular, or neither.

Answer 1

To determine if lines PQ and RS are parallel, perpendicular, or neither, we need to find the slopes of both lines. The slopes of PQ and RS are both -1/4, so the lines are parallel.

Step-by-step explanation:

To determine if lines PQ and RS are parallel, perpendicular, or neither, we need to find the slopes of both lines. The slope of a line can be found using the formula: slope = (change in y-coordinates) / (change in x-coordinates).

Using the coordinates given:

• PQ: slope = (1 - 2) / (2 - (-2)) = -1/4
• RS: slope = (-2 - (-1)) / (5 - 1) = -1/4

Since both lines have the same slope (-1/4), they are parallel.

To determine if lines PQ and RS are parallel, perpendicular, or neither, we need to calculate the slopes of both lines. The slope of a line passing through points (x1, y1) and (x2, y2) is given by (y2 - y1)/(x2 - x1). For line PQ:

Slope of PQ = (1 - 2)/(2 - (-2)) = -1/4

For line RS:

Slope of RS = (-2 - (-1))/(5 - 1) = -1/4

Since both slopes are equal, lines PQ and RS are parallel to each other.