Worked examples
The question
Question: translate the point P(2, 3) left 4.
P = (2, 3)
= left 4
1 Draw the shape
Put the point on the grid.
2 Read the move
Left 4 means x gets 4 smaller: x − 4.
Left 4 → x − 4
We do not go up or down.
So y stays the same.
y stays the same
So every point (x, y) goes to (x − 4, y).
(x, y) → (x − 4, y)
3 Move each point
Start at P.
Go left 4.
We land on the new point.
We call the new point P prime.
The little mark means: the new P.
P is (2, 3).
Left 4: 2 minus 4 is −2.
Y stays 3.
So P' is (−2, 3).
P(2, 3) → (2 − 4, 3) = P'(−2, 3)
Careful!
Left makes x smaller.
So we take 4 away.
We do not add it.
Careful: not P'(2 + 4, 3) ✗
4 The new point
So the image is P'(−2, 3).
P' = (−2, 3)
5 Check
Let's check.
Draw an arrow from each point to its new point.
The arrow goes left 4.
Right!
P → P': left 4
Let's look back.
First: draw the shape.
Then: read the move.
Then: move each point.
Then: the new point.
Last: check.
▶ Watch it solved
The question
Question: translate the shape A(1, 1), B(4, 1) and C(1, 3) right 3, down 2.
A(1, 1), B(4, 1) and C(1, 3)
= right 3, down 2
1 Draw the shape
Put the points on the grid and join them.
2 Read the move
Right 3 means x gets 3 bigger: x + 3.
Right 3 → x + 3
Down 2 means y gets 2 smaller: y − 2.
Down 2 → y − 2
So every point (x, y) goes to (x + 3, y − 2).
(x, y) → (x + 3, y − 2)
3 Move each point
Start at A.
Go right 3.
Then go down 2.
We land on the new point.
We call the new point A prime.
The little mark means: the new A.
A is (1, 1).
Right 3: 1 plus 3 is 4.
Down 2: 1 minus 2 is −1.
So A' is (4, −1).
A(1, 1) → (1 + 3, 1 − 2) = A'(4, −1)
Careful!
Down makes y smaller.
So we take 2 away.
We do not add it.
Careful: not A'(1 + 3, 1 + 2) ✗
Now B: 4 plus 3 is 7.
1 minus 2 is −1.
So B' is (7, −1).
B(4, 1) → (4 + 3, 1 − 2) = B'(7, −1)
Now C: 1 plus 3 is 4.
3 minus 2 is 1.
So C' is (4, 1).
C(1, 3) → (1 + 3, 3 − 2) = C'(4, 1)
4 Draw the image
Join the new points.
This new shape is called the image.
So the image is A'(4, −1), B'(7, −1) and C'(4, 1).
A'(4, −1), B'(7, −1) and C'(4, 1)
5 Check
Let's check.
Draw an arrow from each point to its new point.
All the arrows are the same: the same length, the same way.
So the shape slid, without turning.
Right!
A → A', B → B', C → C': right 3, down 2
Let's look back.
First: draw the shape.
Then: read the move.
Then: move each point.
Then: draw the image.
Last: check.
Answer A'(4, −1), B'(7, −1) and C'(4, 1)
▶ Watch it solved
The question
Question: translate the shape A(1, 1), B(4, 1), C(4, 3) and D(1, 3) left 2, down 5.
A(1, 1), B(4, 1), C(4, 3) and D(1, 3)
= left 2, down 5
1 Draw the shape
Put the points on the grid and join them.
2 Read the move
Left 2 means x gets 2 smaller: x − 2.
Left 2 → x − 2
Down 5 means y gets 5 smaller: y − 5.
Down 5 → y − 5
So every point (x, y) goes to (x − 2, y − 5).
(x, y) → (x − 2, y − 5)
3 Move each point
Start at A.
Go left 2.
Then go down 5.
We land on the new point.
We call the new point A prime.
The little mark means: the new A.
A is (1, 1).
Left 2: 1 minus 2 is −1.
Down 5: 1 minus 5 is −4.
So A' is (−1, −4).
A(1, 1) → (1 − 2, 1 − 5) = A'(−1, −4)
Careful!
Down makes y smaller.
So we take 5 away.
We do not add it.
Careful: not A'(1 − 2, 1 + 5) ✗
Now B: 4 minus 2 is 2.
1 minus 5 is −4.
So B' is (2, −4).
B(4, 1) → (4 − 2, 1 − 5) = B'(2, −4)
Now C: 4 minus 2 is 2.
3 minus 5 is −2.
So C' is (2, −2).
C(4, 3) → (4 − 2, 3 − 5) = C'(2, −2)
Now D: 1 minus 2 is −1.
3 minus 5 is −2.
So D' is (−1, −2).
D(1, 3) → (1 − 2, 3 − 5) = D'(−1, −2)
4 Draw the image
Join the new points.
This new shape is called the image.
So the image is A'(−1, −4), B'(2, −4), C'(2, −2) and D'(−1, −2).
A'(−1, −4), B'(2, −4), C'(2, −2) and D'(−1, −2)
5 Check
Let's check.
Draw an arrow from each point to its new point.
All the arrows are the same: the same length, the same way.
So the shape slid, without turning.
Right!
A → A', B → B', C → C', D → D': left 2, down 5
Let's look back.
First: draw the shape.
Then: read the move.
Then: move each point.
Then: draw the image.
Last: check.
Answer A'(−1, −4), B'(2, −4), C'(2, −2) and D'(−1, −2)
▶ Watch it solved
