Question

Prove that ABCD is a square if a A(1,3) B(2,0) C(5,1) and D(4,4)

Answer 1

$AB=BC=CD=AD = \sqrt{10}$

As all the sides have same length, ABCD is a square

Step-by-step explanation:

To prove ABCD a square we have to find the lengths of each side

So,

the distance formula will be used to find the lengths

The distance formula is:

$d = \sqrt{(x_2-x_1)^2+(y_2-y_1)^2}$

Now,

$AB = \sqrt{(2-1)^2+(0-3)^2}\\= \sqrt{(1)^2+(-3)^2}\\=\sqrt{1+9}\\=\sqrt{10}$

$BC = \sqrt{(5-2)^2+(1-0)^2}\\= \sqrt{(3)^2+(1)^2}\\=\sqrt{9+1}\\=\sqrt{10}$

$CD = \sqrt{(4-5)^2+(4-1)^2}\\= \sqrt{(-1)^2+(3)^2}\\=\sqrt{1+9}\\=\sqrt{10}$

$AD = \sqrt{(4-1)^2+(4-3)^2}\\= \sqrt{(3)^2+(1)^2}\\=\sqrt{9+1}\\=\sqrt{10}$

we can see that

$AB=BC=CD=AD = \sqrt{10}$

As all the sides have same length, ABCD is a square

Keywords: Distance formula, square

Learn more about coordinate geometry at:

• brainly.com/question/7207785
• brainly.com/question/7265276

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