Determine the value of y so that the line segment with endpoints P(3, y) and Q(-3, -1) is parallel to the line segment with endpoints R(-4, 9) and S(5,6).
same slope
(6-9) / (5+4) = (-1-y) / (-3-3)
To determine the value of y, we need to find the slope of the line segment PQ and compare it to the slope of the line segment RS. If the two segments are parallel, their slopes will be equal.
The slope of a line can be found using the formula:
slope = (y2 - y1) / (x2 - x1)
For the line segment PQ, its coordinates are P(3, y) and Q(-3, -1). So, the slope of PQ is:
slope_PQ = (-1 - y) / (-3 - 3)
For the line segment RS, its coordinates are R(-4, 9) and S(5, 6). So, the slope of RS is:
slope_RS = (6 - 9) / (5 - (-4))
To make the line segments parallel, we need the slopes of PQ and RS to be equal. Therefore, we can set up the equation:
slope_PQ = slope_RS
(-1 - y) / (-3 - 3) = (6 - 9) / (5 - (-4))
Now we can solve this equation to find the value of y.