Question

A (1, -3) B (1, 0) C (4, 2) Parallelogram ABCD has the coordinates: Find the coordinates of point D.

Answer 1

Answer:

(4,-1)

Step-by-step explanation:

Given

3 Co-ordinates of a parallelogram ABCD

A=(1,-3)

B=(1,0)

C=(4,2)

D=(a,b)

One of the property of a parallelogram is that the diagonals bisect each other

In this case, AC and BD bisect each other, Therefore the middle point of AC and BD coincide

⇒Mid-point of AC= Mid-point of BD

(mid point of 2 points (x,y) and (k,l) is $=(\frac{(k+x)}{2} ,\frac{(l+y)}{2})$)

$(\frac{(1+4)}{2} ,\frac{(-3+2)}{2})=(\frac{(1+a)}{2} ,\frac{(0+b)}{2})\\(\frac{5}{2} ,\frac{-1}{2})=(\frac{(1+a)}{2} ,\frac{b}{2})$

Compare x and y co-ordinates on both sides

⇒$\frac{5}{2} =\frac{1+a}{2}$

a=4

⇒$\frac{-1}{2}=\frac{b}{2} }$

b=-1

Therefore D=(4,-1)