Given the equations of two adjacent sides of the parallelogram x + y + 5 = 0 and x-4y = 0

Given the equations of two adjacent sides of the parallelogram x + y + 5 = 0 and x-4y = 0 Find the equations of the other two sides if the intersection point of its diagonals K (2; -2) is known.

1. Let us express y in terms of x and find the slopes of the lines:

1)

x + y + 5 = 0;
y = -x – 5; (one)
k1 = -1;
2)

x – 4y = 0;
-4y = -x;
y = 1/4 * x; (2)
k2 = 1/4.
2. Let’s compose the equations of parallel straight lines passing through the point K (2; -2):

y + 2 = k (x – 2);
y = k (x – 2) – 2;
1) k = k1;

y = -1 (x – 2) – 2 = -x + 2 – 2;
y = -x; (3)
2) k = k2;

y = 1/4 (x – 2) – 2 = 1/4 * x – 1/2 – 2;
y = 1/4 * x – 5/2. (four)
3. Draw up the equations of the other parties:

1)

y = -x – 5;
y = -x + 0;
(b1 – 5) / 2 = 0;
b1 = 5;
y = k1x + b1 = -x + 5;
2)

y = 1/4 * x + 0;
y = 1/4 * x – 5/2;
(b2 + 0) / 2 = -5/2;
b2 = -5;
y = k2x + b2 = 1/4 * x – 5.
Answer: y = -x + 5; y = 1/4 * x – 5.