Question

two verticies of paralellogram ABCD are A(-6,-1) and B(-5,3). The intersection of the diagonals, E, are (-2, 1/2). Determine the coordinates of D.

Answer 1

Answer:

D(2,2)

Step-by-step explanation:

The diagonals of a parallelogram gram bisects each other.

Therefore E is the midpoint of AD.

Let the coordinates of D be (a,b).

By the midpoint rule:

$( \frac{x_1+x_2}{2} ,\frac{y_1+y_2}{2}) = ( - 2, \frac{1}{2} )$

This implies that:

$( \frac{ - 6+a}{2} ,\frac{ - 1+b}{2}) = ( - 2, \frac{1}{2} )$

This implies that:

$( \frac{ - 6+a}{2} = - 2 ,\frac{ - 1+b}{2} = \frac{1}{2} )$

$( - 6+a =- 4 , - 1+b = 1 ) \\ ( a =- 4 + 6 , b = 1 + 1 ) \\ ( a =2 , b =2 )$