To solve this problem, we need to find the rule that moves the giraffe from the first graph (on the left) to the second graph (on the right). This is called a
translation or a
slide.
We can figure out the rule by picking one specific point on the first giraffe and seeing where it lands on the second giraffe.
Step 1: Pick a matching point.
Let's look at the very top of the giraffe's head (the tip of the "horn" or ossicone on the left side).
* On the
left graph, find the coordinates of this point.
* Go along the x-axis (horizontal): It is at
-8.
* Go up the y-axis (vertical): It is at
19.
* So, the starting point is
(-8, 19).
* On the
right graph, find the same point on the new giraffe.
* Go along the x-axis: It is at
7.
* Go up the y-axis: It is at
38.
* So, the ending point is
(7, 38).
Step 2: Calculate the change in X (Horizontal Slide).
To get from -8 to 7, we add numbers.
* $7 - (-8) = 15$
* Since the number is positive, we moved
15 units to the right.
Step 3: Calculate the change in Y (Vertical Slide).
To get from 19 to 38, we add numbers.
* $38 - 19 = 19$
* Since the number is positive, we moved
19 units up.
Step 4: Verify with another point.
Let's check the bottom-left corner of the giraffe's front hoof to be sure.
* Left Graph Point:
(-6, -20)
* Right Graph Point: Let's apply our rule (Right 15, Up 19).
* New X: $-6 + 15 = 9$
* New Y: $-20 + 19 = -1$
* Looking at the right graph, the front hoof is indeed at
(9, -1). The rule works!
Conclusion:
The transformation is a translation of
15 units right and
19 units up. In coordinate notation, this is written as $(x + 15, y + 19)$.
Final Answer:
Translation: 15 units right, 19 units up $(x + 15, y + 19)$
Parent Tip: Review the logic above to help your child master the concept of free coordinate graphing mystery picture worksheet.
