coordinate geometry help !!

[maths_arghh234]

question the points A,B,C,D have coordinates (-1,3),(1,7), (2,-1), (5,k) respectively the line AB is parallel to CD

a) find the gradient of AB ... i finished this the gradient was 2
b) show that k=5.. this is where i'm stuck, i don't know how to do this or where to start, please help ! thanks

 

[Mrspi]

question the points A,B,C,D have coordinates (-1,3),(1,7), (2,-1), (5,k) respectively the line AB is parallel to CD

a) find the gradient of AB ... i finished this the gradient was 2
b) show that k=5.. this is where i'm stuck, i don't know how to do this or where to start, please help ! thanks

You are told that line AB is parallel to line CD. What do you know about the gradients (slopes) of two parallel lines?

And how would you represent the gradient of line CD? Would you agree with this as a representation?

(k - (-1)) / (5 - 2)

Once you have found the relationship between the gradients of parallel lines, you can use the gradient you found for AB, and the expression I wrote for the gradient of CD to write an equation...then you can solve that equation to find the value of "k".