Point a(–4, 2) is reflected over the line x = 3 to create the point a'. what are the coordinates of a'?

Coordinates of a' ( 10 , 2).

Step-by-step explanation:

Given : Point a(–4, 2) is reflected over the line x = 3 to create the point a'.

To find :  what are the coordinates of a'.

Solution : We have given that point a(–4, 2)

It is reflected over line   x = 3

By the reflection rule

1) the y-coordinate is unaffected.

(2) for reflections the distance from the line of reflection to the object is equal to the distance to the image point.

a = 4 + 3 = 7.

so the image point is 3 units from the line of reflection

a' = 7 +3 = 10

Then coordinates of a' ( 10 , 2)

Therefore, Coordinates of a' ( 10 , 2).

area of part 1:

a1=base*height/2=(8+2)*(8-2-2-1)/2=10*3/2=15 ft^2

area of part 2:

a2=length*width=(8+2)*1=10 ft2

area of part 3:

a3=length*width=8*2=16 ft2

total shaded area : a1+a2+a3=41 ft2

total area of the reactangle : a=16*8=128 ft2

total area of the nonshaded region : 128-41=87 ft2