Question

If (-6, -4) and (3,5) are the extremities of the diagonal of a parallelogram and (-2, 1) is its third vertex, then its
fourth vertex is​

Answer 1

Answer:

fourth vertex = (-1 , 0)

Step-by-step explanation:

let say fourth vertex = ( x , y)

Then slope of parallell lines are equal

(y - (-4) )/(x - (-6))  =   (5 - 1)/(3 -(-2))

=> (y + 4)/(x + 6)  = 4/5

=> 5y + 20 = 4x + 24

=> 5y = 4x + 4      eq 1

(y - 5)/(x - 3)  = ( -4 - 1)/(-6 -(-2))

=> (y - 5)/(x - 3) = -5/-4

=>  (y - 5)/(x - 3) = 5/4

=> 4y - 20 = 5x - 15

=> 4y = 5x + 5    Eq1

4 * eq 1  = 5 * eq2

=> 16x + 16 = 25x + 25

=> 9x = -9

=> x = -1

& y = 0

fourth vertex = (-1 , 0)