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Question 2: Forming a Rectangle The equation of two adjacent sides of a rectangle are: 1. x - 2y + 8 = 0 and 2.2x + y + 6 = 0

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Answer #1

Solution:

Eq 1: x - 2y + 8 = 0

Eq. 2: 2x + y + 6 = 0

Let's rewrite eq.(1) and (2) n slope intercept form.

Eq. 1) x – 2y + 8 = 0 = y = 5 +& &

Eq. 2) 2x + y +6=0=y= -2.3 - 6

Now,

Equation of line CD is

y = -2.6 - 6

Equation of line AD is

2 y +8

In rectangle ABCD, AB || CD and AD || BC.

Therefore slope of line AB is equal to slope of line CD. Slope of line AD is equal to slope of line BC.

Equation of line AB is

y = -2.2 + C1 .................(3)

Equation of line BC is

y = 3 +62 ...................(4)

Eq. (3) and (4) passes through point (6, 2)

2 = -26)+C1 = C1 = 14

6 2 = 3 + c2= 2 = -1

Therefore,

Equation of line AB is

y = -2.0 + 14

Equation of line BC is

-

Equation of line CD is

y = -2.6 - 6

Equation of line AD is

2 y +8

A B (612) 2x+y+6=0 D X-2y+8=0

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