is the line through points P (-1,-2) and Q(1,2) parallel to the line through the points R(3,-1) and S(5,3)
To determine if the line through points P (-1,-2) and Q(1,2) is parallel to the line through points R(3,-1) and S(5,3), we can calculate the slopes of the two lines.
The slope of a line passing through points (x1, y1) and (x2, y2) can be calculated using the formula:
slope = (y2 - y1)/(x2 - x1)
For the line passing through points P(-1, -2) and Q(1, 2):
slope_PQ = (2 - (-2))/(1 - (-1)) = 4/2 = 2
For the line passing through points R(3, -1) and S(5, 3):
slope_RS = (3 - (-1))/(5 - 3) = 4/2 = 2
The slopes of the two lines are equal, which means that the line through points P (-1,-2) and Q(1,2) is parallel to the line through points R(3,-1) and S(5,3).