Answer:
The area of rectangle is [tex]56\ units^2[/tex]
Step-by-step explanation:
Let
A(2,7)
step 1
The point A is reflected across the x-axis
we know that
The rule of the reflection of a point across the x-axis is
(x,y) -----> (x,-y)
so
A(2,7) ----->B(2,-7)
step 2
The point B is reflected across the y-axis
we know that
The rule of the reflection of a point across the y-axis is
(x,y) -----> (-x,y)
B(2,-7) ----> C(-2,-7)
step 3
The point C is reflected across the x-axis
we know that
The rule of the reflection of a point across the x-axis is
(x,y) -----> (x,-y)
so
C(-2,-7) ----->D(-2,7)
step 4
Find the area of rectangle formed by
A(2,7),B(2,-7),C(-2,-7),D(-2,7)
using a graphing tool
see the attached figure
The area of rectangle is
[tex]A=(4)(14)=56\ units^2[/tex]
