Let P = (3,7), Q = (-4,2), R = (5,1), S = (-16,-14).
Is parallel to?
To determine if two lines are parallel, we need to check if their slopes are equal.
The slope of a line passing through two points (x1, y1) and (x2, y2) is given by the formula:
m = (y2 - y1)/(x2 - x1)
Let's calculate the slopes of the lines passing through the given points:
For line PQ, the slope is:
m(PQ) = (2 - 7)/(-4 - 3) = -5/-7 = 5/7
For line RS, the slope is:
m(RS) = (1 - (-14))/(5 - (-16)) = 15/21 = 5/7
Since the slopes of lines PQ and RS are equal (both are 5/7), we can conclude that they are parallel.
To determine if a pair of lines is parallel, we need to compare their slopes. If the slopes are equal, then the lines are parallel.
Let's find the slopes of the pairs of points (P, Q) and (R, S) to determine if they are parallel.
The formula to calculate the slope between two points (x1, y1) and (x2, y2) is given by:
slope = (y2 - y1) / (x2 - x1)
For the points P = (3,7) and Q = (-4,2), the slope is:
slope(PQ) = (2 - 7) / (-4 - 3) = -5 / -7 = 5/7
For the points R = (5,1) and S = (-16,-14), the slope is:
slope(RS) = (-14 - 1) / (-16 - 5) = -15 / -21 = 5/7
Since the slopes of both pairs of points are equal to 5/7, the lines PQ and RS are parallel.