Question

Question #e2075

Answer 1

Point B has the coordinates `(-(7/3),(-10/3))`

Explanation:

Eqn of line AB is `x—y=-1` & slope of AB`=1`
Eqn of line AD is `7x-y=5` & slope of AD `=7`

Solving Eqn AB & AD, we get point A.
`6x=6` or `x=1` & `y=2`
Point A `(1,2)`

E is the midpoint of A & C
Point E `(-1,-2)`

`(x+1)/2=-1`
`x=-3`
`(y+2)/2=-2`
`y=-6`
Point C`(-3,-6)`

Slope of BC is same as slope of AD `=7`
Eqn of line BC is `y+6=7(x+3)`
`y-7x=5`
Solving line Equations AB & BC, we get point B.
Line AB `x-y=-1`
Line BC `-7x+1=5`
`:.-6x=14` or `x=-(7/3)` & `y=-(10/3)`
Point B `(-(7/3),-(10/3)`

Slope of CD is same as slope of AB `=1`
Eqn of line CD is `(y+6)=(x+3)`
`y-x=-3`
Solving Eans AD & CD, we get point D
Line AD `7x-y=5`
Line CD `y-x=-3`
`:.6x=2` or `x=1/3` & `y=-(8/3)`
Point D`(1/3,-(8/3))`