The question
Question: describe the move that takes A(2, 1) and B(4, 3) to A'(2, −1) and B'(4, −3).
A(2, 1) and B(4, 3)
A'(2, −1) and B'(4, −3)
1 Draw both shapes
Put the shape on the grid
and its image.
2 Compare A and A'
Look at what happened to the numbers of A: A(2, 1) went to A'(2, −1).
A(2, 1) → A'(2, −1)
x stayed the same.
x stays 2
y changed sign.
y: 1 → −1 sign changes
3 Name the move
So the rule is: (x, y) goes to (x, −y).
(x, y) → (x, −y)
Careful!
Only one sign changed.
That is a flip in an axis.
A half turn changes both signs.
Careful: not rotation 180° ✗
That is the rule of a flip in the x-axis.
So the move is a reflection: in the x-axis.
reflection = in the x-axis
4 Check
Let's check the rule on the other points.
B goes to (4, −3).
That is B'.
B(4, 3) → (4, −3) = B'
Let's look back.
First: draw both shapes.
Then: compare A and A'.
Then: name the move.
Last: check.
Answer reflection = in the x-axis
▶ Watch it solved
The question
Question: describe the move that takes A(2, 1), B(4, 1) and C(2, 3) to A'(−1, 2), B'(−1, 4) and C'(−3, 2).
A(2, 1), B(4, 1) and C(2, 3)
A'(−1, 2), B'(−1, 4) and C'(−3, 2)
1 Draw both shapes
Put the shape on the grid
and its image.
2 Compare A and A'
Look at what happened to the numbers of A: A(2, 1) went to A'(−1, 2).
A(2, 1) → A'(−1, 2)
The two numbers swapped places.
2 and 1 swap places
And the new first number got a minus sign.
the new x gets a minus
3 Name the move
So the rule is: (x, y) goes to (−y, x).
(x, y) → (−y, x)
Careful!
A swap alone would be a flip in the line y = x.
Here one number also changed sign.
That is a turn.
Careful: not reflection in y = x ✗
That is the rule of a turn about O.
So the move is a rotation of 90° counterclockwise about the origin.
rotation = 90° counterclockwise
4 Check
Let's check the rule on the other points.
B goes to (−1, 4).
That is B'.
B(4, 1) → (−1, 4) = B'
C goes to (−3, 2): C'.
Right!
C(2, 3) → (−3, 2) = C'
Let's look back.
First: draw both shapes.
Then: compare A and A'.
Then: name the move.
Last: check.
Answer rotation = 90° counterclockwise
▶ Watch it solved
The question
Question: reflect the shape A(1, 1), B(3, 1) and C(1, 4) in the y-axis, then translate it down 2.
A(1, 1), B(3, 1) and C(1, 4)
= reflect in the y-axis,
= then translate down 2
1 Draw the shape
Put the points on the grid and join them.
2 First: reflect in the y-axis
Reflection in the y-axis: x changes sign, y stays the same.
The rule is: (x, y) goes to (−x, y).
(x, y) → (−x, y)
A(1, 1) goes to A'(−1, 1).
A(1, 1) → A'(−1, 1)
B(3, 1) goes to B'(−3, 1).
B(3, 1) → B'(−3, 1)
C(1, 4) goes to C'(−1, 4).
C(1, 4) → C'(−1, 4)
Join them.
This is the first image.
3 Then: translate
Translation down 2: down 2 takes 2 from y.
The rule is: (x, y) goes to (x, y − 2).
(x, y) → (x, y − 2)
A'(−1, 1) goes to A''(−1, −1).
A'(−1, 1) → A''(−1, −1)
Careful!
The second move starts from the new points A', B' and C'.
Not from the first shape.
Careful: start from A', not from A
B'(−3, 1) goes to B''(−3, −1).
B'(−3, 1) → B''(−3, −1)
C'(−1, 4) goes to C''(−1, 2).
C'(−1, 4) → C''(−1, 2)
Join them.
This is the final image.
So the final image is A''(−1, −1), B''(−3, −1) and C''(−1, 2).
A''(−1, −1), B''(−3, −1) and C''(−1, 2)
4 Check
Let's check in one go.
Put the first rule's answer (−x, y) into the second rule.
We get (−x, y − 2).
(x, y) → (−x, y) → (−x, y − 2)
A goes straight to (−1, −1).
That is A''.
Right!
A(1, 1) → A''(−1, −1)
Let's look back.
First: draw the shape.
Then: reflect in the y-axis.
Then: translate down 2.
Last: check.
Answer A''(−1, −1), B''(−3, −1) and C''(−1, 2)
▶ Watch it solved
