Answer: “In geometry we use input/output process when we determine how shapes are altered or moved. Geometric objects can be moved in the coordinate plane using a coordinate rule. These rules can alter the shape in many different ways. Some rules will translate the shape, some will rotate or reflect the shape, some will stretch or distort the shape, some will increase the size of the shape, etc... lots of different things can happen. Look at the example below:
So rule T will move or map all points (x,y) by adding 3 to the x value of each point, and subtracting 6 from each y value of each point
The name of the rule is a capital letter before the (x,y). The point (x,y) represents that all points in
the plane will be effected by this rule. The arrow represents the geometric term of map or mapping,
which is a geometric way of saying moves. Finally the coordinate description after the mapping arrow
symbol represents the change produced by the rule. Can you see the connection to functions? You
will input values into the coordinate rule and it will output new values, just as function did. A change
is that we refer to the input value as the pre-image, the original location of the point, and the output
value as the image, the new location of the point. To help clarify the difference between a pre-
image and an image, we use special notation. If the pre-image is point A, then its image will
be A’ (said A prime). The prime notation tells us that it is an image.
1. Given coordinate rule
T(x,y)→ (x+3,y–6)determinethe pimage of A(-1, 5)? Pre-image Image
T(x, y)------------ (x + 3, y – 6) T(-1, 5) ---------- (-1 + 3, 5 – 6) T(-1,5)--------- (2,-1)
Pre-image A(-1, 5) Image A`(2, -1)
2. Given coordinate rule
G(x,y)→ (2x+3,y+1)determinethe image of B(5, 2)?
Pre-image Image
G(x, y)-------------(2x, y + 1) G(5, 2)-------------(2(5), 2 + 1) G(5, 2)------------(10, 3)
Pre-image B(5, 2) Image B`(10, 3)
Working backwards is performing the inverse operation. + ↔ - and x ↔ ÷
3. Given coordinate rule
T(x,y)→ (x+3,y–6)determine the pre-image of C`(3, 2)? Pre-image Image
T(x, y) (x + 3, y – 6) 3=x+3 2=y–6
-3 -3 +6 +6
x=0 y=8 Pre-image C(0, 8) Image C`(3, 2)
4. Given coordinate rule
T(x, y) → (2x, y + 1) determine the the pre-image of D`(-4, 11)?
Pre-image T(x, y)
2x = -4
22 -1-1
x = -2 y = 10 Pre-image D(-2, 10) Image D`(-4, 11)“
Step-by-step explanation:
