Question

Prove that points (-2. 1). (1.0), (4.3) and (1, 2) are the vertices of a parallelogram. Is it a
rectangle​

Answer 1

Answer:

∴AB=CD= 10

​and BC=AD= 18

​ The opposite sides of the quadrilateral ABCD are equal, the four points from a parallelogram.

Step-by-step explanation:

Given points are

A(−2,−1),B(1,0),C(4,3) and D(1,2)

A quadrilateral is a parallelogram if the opposite sides are equal.

∴AB

2

=(−2−1)

2

+(−1−0)

2

=9+1

=10

BC

2

=(4−1)

2

+(3−0)

2

=9+9

=18

CD

2

=(1−4)

2

+(2−3)

2

9+1

=10

AD

2

=(−2−1)

2

+(−1−2)

2

=9+9

=18

Answer 2

Answer:

Step-by-step explanation:

Correct question :-

A= (-2 , 1) , B=(1 , 0)  , C = (4 , 3) , D = (1 , 4) are the vertices of a parallelogram.

Condition Required To Prove :-

We need to prove that the mid-point of AC and mid-point of BD are same i.e we need to prove Origin(O) is same.

Formula Required :-

$Mid-point=\left(\dfrac{x_1+x_2}{2},\dfrac{y_1+y_2}{2}\right)$

Solution :-

A = (-2 , 1) = ( x_1 , y_1)

C = (4 , 3) = (x_2 , y_2)

$Mid-point=\left(\dfrac{-2+4}{2},\dfrac{1+3}{2}\right)$

$=\left(\dfrac{2}{2},\dfrac{4}{2}\right)$

= (1 , 2)

B = (1 , 0) = (x_1 , y_1)

D = (1 , 2) = (x_2 , y_2)

$Mid-point=\left(\dfrac{1+1}{2},\dfrac{0+4}{2}\right)$

$=\left(\dfrac{2}{2},\dfrac{4}{2}\right)$

= (1 , 2)

Hence Proved that mid-points are same so it a parallelogram