Answer to Question #178936 in Analytic Geometry for John withers

Question

 𝑊𝑋𝑌𝑍 is a parallelogram with 𝑊(0, −3), 𝑋(5, −1), and 𝑌(3, −4). Find the coordinates of point 𝑍. Recall that parallelogram points are listed in clockwise order.

Answer 1

WXYZ

W(x,y) =(0,-3) ,X(x, y)=(5,-1) ,Y(x, y)=(3,-4) , Z(x, y)=(x₁,y₁)

parallelogram opposite sides are equal:

W-X=Y-Z AND W-Z=X-Y

W-Z= x _x-x_w and y=y_x -y_w , 5-0=5 , -1-(-3)=2

therefore difference is (5,2) implying:

Y-Z= x_y-x_z=5 and y_y-y_z=2

3-x_z=5 and -4-y_z =2

hence Z=(-2,-6)