Question

ABCD is a parallelogram in which A =(1,4), B =(5,8) and C = (6,-3). Find the fourth vertex D.

Answer 1

Answer:

✿solution✿☘️

given;

let A(1,4) ,B(5,8), C(6,-3) be the three given vertics of llgm of ABCD

to find ;

find the coordinates of fourth vertics

now;

join AC and BD

let ,AC and BD intreact at "O"

we know that the diagonal of a llgm bisect each other

so , "O" is the midpoint of each one of AC and BD

midpoint of AC is =

$( \frac{1 + 6}{2} . \frac{4 + - 3}{2}) \\ ( \frac{7}{2} . \frac{1}{2} )$

and the midpoint of BD

$( \frac{5 + a}{2} . \frac{8 + b}{2} ) \\ \\ \frac{7}{2} = \frac{5 + a}{2} = 7 = 5 + a \\ a = 2 \\ \\ \frac{1}{2} = \frac{8 + b}{2} \\ \\ 1 = 8 + b \\ b = - 7$

hence, fourth vertics of llgm ABCD is D (2,-7)