Question

L (-1,-1) M (0,0) N (3,0) Parallelogram LMNO has the coordinates shown. Find the coordinates of point O.

Answer 1

The coordinates of point O are (2,-1).

Explanation:

The opposites sides of parallelogram are parallel to each other and the slopes of parallel lines are equal.

Slope formula

`m=(y_2-y_1)/(x_2-x_1)`

Let the coordinates of point O be (x,y).

The sides LM and NO are parallel to each other. So, the slope of LM is equal to slope of LM.

`m_(LM)=m_(NO)`

`(0-(-1))/(0-(-1))=(0-b)/(3-a)`

`(1)/(1)=(-b)/(3-a)`

`3-a=-b`

`3=a-b` .... (1)

The sides LO and MN are parallel to each other. SO, the slope of LO is equal to slope of MN.

`m_(LO)=m_(MN)`

`(b-(-1))/(a-(-1))=(0-0)/(3-0)`

`(b+1)/(a+1)=0`

`b+1=0`

`b=-1`

Therefore the value of b is -1.

Put b=-1 in equation 1.

`3=a-(-1)`

`3=a+1`

`a=2`

The value of a is 2. Therefore the coordinates of point O are (2,-1).