Question

A (1, 1)
B (1, 3)
C (4, 3)
Rectangle ABCD has the coordinates shown.

Find the coordinates of point D.
A) (5, 1)
B) (4, 2)
C) (3, 1)
D) (4, 1)

Answer 1

The answer is D.......

Answer 2

Answer:

The coordinate of D is (4,1)

D is correct

Step-by-step explanation:

A (1, 1)  

B (1, 3)  

C (4, 3)

ABCD is a rectangle.

Let coordinate of D be (x,y)

As we know mid point of both diagonal is same.

In rectangle ABCD

Diagonals are AC and BD.

So, Mid point of AC =  Mid point of BD

Formula:

$\text{Mid-Point }=(\dfrac{x_1+x_2}{2},\dfrac{y_1+y_2}{2})$

$\text{Mid-Point of AC }=(\dfrac{1+4}{2},\dfrac{1+3}{2})\rightarrow (\frac{5}{2},2)$

$\text{Mid-Point of BD }=(\dfrac{1+x}{2},\dfrac{y+3}{2})$

$\dfrac{1+x}{2}=\dfrac{5}{2}\Rightarrow x=4$

$\dfrac{y+3}{2}=2\Rightarrow y=1$

Hence, The coordinate of D is (4,1)