Do the points lie on the same line? Explain your answer.
P(4,4), Q(-1,2), R(-3,3)
To determine whether the points lie on the same line, we can calculate the slopes of the lines formed by any two of the points. If the slopes are equal, then the points are collinear (i.e., lie on the same line).
Let's first calculate the slopes of the lines formed by P and Q, and P and R:
Slope of line PQ = (y2 - y1) / (x2 - x1)
= (2 - 4) / (-1 - 4)
= -2 / -5
= 2/5
Slope of line PR = (y2 - y1) / (x2 - x1)
= (3 - 4) / (-3 - 4)
= -1 / -7
= 1/7
Since the slopes of the lines formed by the pairs of points do not match (2/5 ≠ 1/7), the points P, Q, and R do not lie on the same line.