A focused Grade 6 learning session for Transformations on the Coordinate Plane using visual models, worked examples, strategy guidance, and a short mastery check.
Student goal: I can solve problems involving transformations on the coordinate plane.
Transformations on the Coordinate Plane means choosing a model, naming what each number means, and explaining the strategy.
Question: A point \(B\) at \((2,1)\) is reflected over the \(y\)-axis. What are the coordinates of \(B'\)?
Why it works: Reflecting over the \(y\)-axis: negate the \(x\)-coordinate. So \((2,1) \to (-2,1)\).
Answer: \((-2,1)\)
Question: A triangle has vertices at \(P(1,2)\), \(Q(3,2)\), and \(R(2,4)\). If the triangle is translated \(3\) units right and \(1\) unit up, what are the coordinates of the image vertex \(P'\)?
Answer: \((4,3)\)
Question: Point \(C\) is at \((-2,-3)\). When it is reflected over the \(y\)-axis, which of the following is its image?
Answer: \((2,-3)\)
Question: Point \(A\) is located at \((3,5)\). If it is translated \(4\) units to the left and \(2\) units down, what are the coordinates of its image \(A'\)?
Why it works: Translate left by subtracting from \(x\): \(3-4=-1\). Translate down by subtracting from \(y\): \(5-2=3\). So \(A'=(-1,3)\).
Answer: \((-1,3)\)
Transformations on the Coordinate Plane becomes easier when students connect the question to a model, use clear steps, and explain why the answer fits.
Understand the model before choosing the operation.
Use scratch paper. The explanation matters more than simply seeing whether the choice is correct.
Point \(A\) is located at \((3,5)\). If it is translated \(4\) units to the left and \(2\) units down, what are the coordinates of its image \(A'\)?
Answer A: \((-1,3)\)
Translate left by subtracting from \(x\): \(3-4=-1\). Translate down by subtracting from \(y\): \(5-2=3\). So \(A'=(-1,3)\).
A point \(B\) at \((2,1)\) is reflected over the \(y\)-axis. What are the coordinates of \(B'\)?
Answer B: \((-2,1)\)
Reflecting over the \(y\)-axis: negate the \(x\)-coordinate. So \((2,1) \to (-2,1)\).
Which point, when reflected over the \(x\)-axis, results in \((4,-3)\)?
Answer A: \((4,3)\)
Reflecting over the \(x\)-axis negates the \(y\)-coordinate. If the image is \((4,-3)\), the original is \((4,3)\).
A triangle has vertices at \(P(1,2)\), \(Q(3,2)\), and \(R(2,4)\). If the triangle is translated \(3\) units right and \(1\) unit up, what are the coordinates of the image vertex \(P'\)?
Answer A: \((4,3)\)
Translation: add \(3\) to \(x\) and \(1\) to \(y\). \(P(1,2) \to P'(1+3, 2+1) = P'(4,3)\).
Point \(C\) is at \((-2,-3)\). When it is reflected over the \(y\)-axis, which of the following is its image?
Answer D: \((2,-3)\)
Reflection over the \(y\)-axis negates the \(x\)-coordinate only: \((-2,-3) \to (2,-3)\).
A square \(ABCD\) has vertices at \((1,1)\), \((3,1)\), \((3,3)\), and \((1,3)\). If the square is translated \(2\) units left, which will be the image of vertex \(C\)?
Answer A: \((1,3)\)
Translating left subtracts from \(x\): \(C(3,3) \to C'(3-2, 3) = C'(1,3)\).
Triangle \(PQR\) is shown with vertices at \(P(1,1)\), \(Q(4,1)\), and \(R(2,3)\). If the triangle is reflected over the \(x\)-axis, what will be the coordinates of \(R'\)?
Answer A: \((2,-3)\)
Reflection over the \(x\)-axis negates the \(y\)-coordinate: \(R(2,3) \to R'(2,-3)\).
Point \(M\) is at \((5,-2)\). If it is translated \(5\) units left and \(3\) units up, what are the coordinates of \(M'\)?
Answer A: \((0,1)\)
Translate left: \(5-5=0\). Translate up: \(-2+3=1\). So \(M' = (0,1)\).
A point \((6,2)\) is reflected over the \(y\)-axis. Where does the image point appear?
Answer A: \((-6,2)\)
Reflection over the \(y\)-axis changes the sign of the \(x\)-coordinate: \((6,2) \to (-6,2)\).
A rectangle with vertices at \(A(0,2)\), \(B(2,2)\), \(C(2,4)\), and \(D(0,4)\) is translated \(1\) unit right and \(2\) units down. What are the coordinates of the image of vertex \(A\)?
Answer A: \((1,0)\)
Translation: \(A(0,2) \to A'(0+1, 2-2) = A'(1,0)\).
If a point at \((-3,-1)\) is reflected over the \(x\)-axis, which of the following is the image?
Answer A: \((-3,1)\)
Reflection over the \(x\)-axis negates the \(y\)-coordinate only: \((-3,-1) \to (-3,1)\).
