ABCD is a parallogram. The coordinat of A,B and C are (4,1), (1,-2), (-2,1) respecitively . Find: a) the equation of AD?

Question

I need help with this maths question. Please go thoroughly through the answer 
the answer btw is y= -x + 5 
how would i find out the equation though 
b) asks for equation of CD 
c) the coordinates of D 

Mainly i would like to know how would i find out the coordinates of D

Answer 1

Parallelgram coordinates are A (4,1) ,B (1,-2), C(-2,1)

ABCD is parallelgram AB , CD and BC, AD are two pair of  parallel sides with equal lengths.

a ) To find the equation of AD

BC and AD are paralllel.

We know that parallel lines are equal slope.

So slope of AD is  -1.

Line equation(AD) in point slope form

b) To find equation of CD

CD and AB are paralllel.

So slope of CD is  1.

Line equation(CD) in point slope form

c) To find the coordinates of D.

Point D will be were AD and CD cross which can be found via solve the simulations equation of those two lines.

From equation (1) substitute the y value in equation (2).

substitute the x value in equation (2).

Coordinates of D = (x ,y ) = (1,4)

We can find also coordinates of D in graphical method.

Draw the coordinate plane.

Plot the points and connect the parallegoram.

Coordinates of D = (1,4)