PQ and RS are two parallel lines. If the coordinates of P, Q, R, S are (1,q), (3,2), (3,4), (5,2q) respectively, find the value of q

Answer Details

Given that PQ and RS are two parallel lines, we can observe that their slopes are equal. The slope of PQ can be found using the coordinates of points P and Q: slope of PQ = (2 - q)/(3 - 1) = (2 - q)/2 Similarly, the slope of RS can be found using the coordinates of points R and S: slope of RS = (2q - 4)/(5 - 3) = (2q - 4)/2 Since PQ and RS are parallel, their slopes are equal: (2 - q)/2 = (2q - 4)/2 Simplifying the equation above, we get: 2 - q = q - 2 2q = 4 q = 2 Therefore, the value of q is 2, which corresponds to.