Line segments AB and CD are parallel. Coordinate A is (4,-1), B is (-2,2), C is (-6,8), and D is (4,K). What is the value of K?

Answer 1

Parallel lines have the same slope, so we can equate the two slopes and solve for K.

(2 - (-1)) / (-2 - 4) = (K - 8) / (4 - (-6))

-3/6 = (K - 8)/10

-30 = 6K - 48

18 = 6K

3 = K

Answer 2

We know that parallel lines have the same slope. Therefore, we can calculate the slope of each, and set them equal to each other to find the value for K.

The formula to find slope is the change in y over the change in x:

For line segment AB:

y2-y1/x2-x1

(2-(-1))/(-2-4)

3/-6

-1/2

For line segment CD:

y2-y1/x2-x1

(K-8)/(4-(-6))

(K-8)/10

We can now set those two slopes equal to each other and solve for K:

-1/2=(K-8)/10

-5=K-8

3=K

Hope this helps!