Question

if (5,-4) and (-3,2) are the two opposite vertices of a square then find its area

Answer 1

Answer:

100 square units .

Step-by-step explanation:

Given: $(x_1,y_1)=(5,-4)$

           $(x_2,y_2)=(-3,2)$

Solution:

Since we know that the sides of square are equal .

To find the length of the side of the square , we will use distance formula:

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

$d=\sqrt{-3-5)^{2}+(2-(-4))^{2}}$

$d=\sqrt{-8)^{2}+(6)^{2}}$

$d=\sqrt{64+36}$

$d=\sqrt{100}$

$d=10$

Thus the side of square is 10 units .

Formula of area of square = $(Side)^2$

So, area of square =  $(10)^2$

                              = 100 square units .

Hence the are of square is 100 square units .