Question

the coordinates of A & B are (3k,8) and (k,-3) respectively. Given that the gradient of the line segment AB is 3, find the value of K

Answer 1

Given

A = (3k,8)

B = (k, -3)

Gradient AB = 3

And we have that the gradient of a line joining the two points A and B is:

`\text{Gradiente AB=}(y2-y1)/(x2-x1)`

Therefore, we substitute the given values into the gradient equation:

Gradient AB = 3

x1 = 3k

y1 = 8

x2 = k

y2 = -3

`3=(-3-8)/(k-3k)`

Then, solve for k.

Simplify:

`3=(-11)/(-2k)=(11)/(2k)`

Multiply by 2k on both sides:

`\begin{gathered} 2k\cdot3=2k\cdot(11)/(2k) \\ 6k=11 \end{gathered}`

Divide by 6 on both sides:

`\begin{gathered} (6k)/(6)=(11)/(6) \\ k=(11)/(6) \end{gathered}`

Answer: k = 11/6