Question

rectangle gift has vertices with the coordinates g(-2,9), i(-8,3), f(5,-10), and t(11,-4).
find the area of rectangle gift.
round your answer to the nearest whole number.
use the keypad to enter the answer in the box provided.
the area of rectangle gift is square units.

Explanation:

Step1: Calculate the length of \( GI \)

Use the distance formula \( d=\sqrt{(x_2 - x_1)^2+(y_2 - y_1)^2} \).
For \( G(-2,9) \) and \( I(-8,3) \), \( x_1=-2,y_1 = 9,x_2=-8,y_2 = 3 \).
\( GI=\sqrt{(-8+2)^2+(3 - 9)^2}=\sqrt{(-6)^2+(-6)^2}=\sqrt{36 + 36}=\sqrt{72}=6\sqrt{2}\)

Step2: Calculate the length of \( IF \)

For \( I(-8,3) \) and \( F(5,-10) \), \( x_1=-8,y_1 = 3,x_2=5,y_2=-10 \).
\( IF=\sqrt{(5 + 8)^2+(-10 - 3)^2}=\sqrt{13^2+(-13)^2}=\sqrt{169+169}=\sqrt{338}=13\sqrt{2}\)

Step3: Calculate the area of the rectangle

The area of a rectangle \( A = l\times w \). Here \( l = IF,w=GI \)
\( A=6\sqrt{2}\times13\sqrt{2}\)
Using the property \( \sqrt{a}\times\sqrt{a}=a \) and \( (a\times b)\times(c\times d)=(a\times c)\times(b\times d) \), we have \( A=(6\times13)\times(\sqrt{2}\times\sqrt{2})=78\times2 = 156\)

Answer:

\(156\)