James is building a house on the lot shown below. The dimensions of the lot are (6+x) feet and (6−x) feet. The blue prints show the dimensions of the house to be (2+x) feet and (2−x) feet. The rest of the lot will be his yard. How large is the yard?
square feet

James is thinking about extending the house by adding 2 feet to the length and 2 feet to the width.

How much area is now left for the yard?
square feet

Step-by-step explanation:

Given

Area of the yard = Area of the lot - Area of the house

Area of the yard:

If the house is extended, then the area of the yard will change as:

for the friend request.

when a figure, such as triangle (xyz) is reflected over the line y = x to create x'y'z' the x-coordinates and y-coordinates of the original image (pre-image) will be reversed for the image. (e.g., (x, y) > (y, x)) this means that the pre-image position of the x- and y-coordinates switch places which in turn provides a mirror like image of the original xyz.  

i notice that when i draw a line segment from x to x', that the points are parallel from each other -- they are exactly across from each other and do not intersect with any other points.  

yes, think i would see the same characteristic if you drew the line segment connecting y with the reflecting line and then y' with the reflecting line because of the essence of reflections. because it is a mirror image, each point was effected the same way which leads me to conclude that they same would apply to y and y'.