Question

Lines~kx+(k+3)y=7 and (k + 4)x + (7k+1)y=10 represent opposite sides of a parallelogram, then the value of k can be
a) 4/3
b) 1
c) 2
d) -2​

Answer 1

Answer:

The given equation of line is

(k−3)x−(4−k

2

)y+k

2

−7k+6=0

(a) If the given line is parallel to the x-axis, then

slope of the given line= slope of the x-axis =0

⇒

(4−k

2

)

(k−3)

=0

⇒k−3=0

⇒k=3

Thus, if the given line is parallel to the x-axis, then the value of k is 3.

(b) If the given line is parallel to the y-axis, it is vertical, hence,its slope will be undefined.

The slope of the given line is

(4−k

2

)

(k−3)

Now,

(4−k

2

)

(k−3)

is undefined at k

2

=4

⇒k=±2

Thus, if the given line is parallel to the y-axis,then the value of k is ±2.

Answer 2

Step-by-step explanation:

Lines~kx+(k+3)y=7 and (k + 4)x + (7k+1)y=10 represent opposite sides of a parallelogram, then the value of k can be

a) 4/3

b) 1

c) 2

d) -2

→c) 2