Ihave this question on the equation of a line,
abcd is a rectangle
a = (7,1) b= (3,4) c= (8, k)
what is the value of k?
instead of telling me the answer could you tell me how i would go about answering this question and give me a simple "step-by-step" so i can do it again and explain to my friend from school how to do it
(ps: gradient ab= 5)

Hello, 

We have the rectangle ABCD, we know that all the angles of a rectangle are 90º, that means that its consecutive lines are perpendicular.

We also know that the slope of a perpendicular line is the inverse negative, i'm going to make and example, so you can understand:

If a line have a slope: m=a 
Its perpendicular line's slope is: 

So, the firs thing we have to do is to find the slope of the line AB, the formula of the slope is:  

So its perpendicular line has the following slope: 

Now, the general formula of the line is: 

We apply it, with the point B and the slope: mBC, so:



This is the function that represents the line BC, We know that the point C is part of the line, then it must meet the equality, so we replace this point and get K:



If I just explained it, you wouldn't have understood it, that's why I solved it, I hope you undestand, If you have any question, don't hesitate to tell me.

K=32/3