A focused Grade 7 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 is part of Grade 7 Geometry and Scale. This activity focuses on the central idea students need before they move into independent practice.
Students will build Grade 7 mastery of transformations on the coordinate plane using models, equations, and test-style reasoning.
| What to notice | How to use it |
|---|---|
| Numbers, units, labels, diagrams, or graphs | Identify what each part represents before calculating. |
| The relationship in the problem | Connect the model to an equation, comparison, or explanation. |
Use the figures and worked questions in the practice set below as the visual model for this skill.
Read the first practice question slowly. Decide what the question is asking, choose a strategy, solve, and then compare your reasoning with the answer explanation.
For Transformations on the Coordinate Plane, a strong worked example should show the setup, the calculation or model, and a final answer that matches the context.
Many Grade 7 test questions use real situations. Look for quantities, units, rates, measures, expressions, or data values that connect the math to the story.
After solving, explain what the answer means in the situation, not just the number you calculated.
I can solve problems involving transformations on the coordinate plane.
Use the warmup, guided question, practice set, and exit questions below to check whether this skill is ready or needs more practice.
Use scratch paper. The explanation matters more than simply seeing whether the choice is correct.
Point \(P(4,-3)\) is reflected over the \(x\)-axis. What are the coordinates of the image \(P'\)?
Answer C: \((4,3)\)
A reflection over the \(x\)-axis flips the sign of the \(y\)-coordinate: \((4,-3)\to(4,3)\).
Which transformation moves the point \(Q(-5, 2)\) to \(Q'(5, 2)\)?
Answer B: Reflection over the \(y\)-axis
Reflection over the \(y\)-axis uses the rule \((x, y)\to(-x, y)\). The \(x\)-coordinate changes sign; the \(y\)-coordinate stays the same. So \((-5, 2)\to(5, 2)\). Check: (A) Translation by \((5, 0)\) gives \((-5+5, 2)=(0, 2)\), not \((5, 2)\). (C) Reflection over \(x\)-axis gives \((-5, -2)\). (D) 180° rotation gives \((5, -2)\).
A triangle with vertices at \(A(1,1)\), \(B(3,1)\), and \(C(2,3)\) is translated by the vector \((2, -4)\). What is the image of vertex \(B\) after this translation?
Answer A: \((5,-3)\)
A translation by \((2, -4)\) adds the vector to each point: \((3, 1)+(2, -4)=(5, -3)\).
Point \(R(2, 5)\) is reflected over the line \(y=x\). What are the new coordinates?
Answer A: \((5, 2)\)
Reflection over \(y=x\) uses the rule \((x, y)\to(y, x)\), swapping the coordinates: \((2, 5)\to(5, 2)\).
Which of the following is an example of a rigid transformation (one that preserves distance and angles)?
Answer A: Reflection over the \(x\)-axis
A rigid transformation preserves all distances and angles. Reflection, rotation, and translation are rigid. Dilation (option B) and shearing (option D) change size or shape, so they are not rigid.
A quadrilateral \(ABCD\) has vertices \(A(0,0)\), \(B(4,0)\), \(C(4,3)\), and \(D(0,3)\). If the quadrilateral is translated by \((-2, 1)\), which of the following is the new location of vertex \(C\)?
Answer A: \((2, 4)\)
Applying the translation vector to \(C(4, 3)\): \((4, 3)+(-2, 1)=(2, 4)\).
Which transformation maps the blue figure (pre-image) to the red figure (image)?
Answer B: Reflection over the \(y\)-axis
The blue square at \(x\in[1,3]\) maps to the red square at \(x\in[-3,-1]\). This is a reflection over the \(y\)-axis.
A line segment has endpoints at \((1, 2)\) and \((4, 2)\). After a reflection over the \(x\)-axis, what is the length of the reflected segment?
Answer A: 3 units
Reflection over the \(x\)-axis preserves distances (it is a rigid transformation). The original segment from \((1, 2)\) to \((4, 2)\) has length \(|4-1|=3\). After reflection to \((1, -2)\) and \((4, -2)\), the length remains 3.
Which transformation maps the purple triangle to the orange triangle?
Answer A: Reflection over the \(x\)-axis
The purple triangle vertices have \(y\)-values \(1, 1, 3\), which become \(-1, -1, -3\) in the orange triangle, indicating a reflection over the \(x\)-axis.
A polygon is translated by the vector \((3, -5)\). One vertex of the original polygon is at \((-1, 4)\). Where is this vertex after the translation?
Answer A: \((2, -1)\)
Adding the translation vector: \((-1, 4)+(3, -5)=(2, -1)\).
If point \(U(7, 0)\) is reflected over the \(y\)-axis, what is the image \(U'\)?
Answer B: \((-7, 0)\)
Reflection over the \(y\)-axis changes \((x, y)\) to \((-x, y)\). So \((7, 0)\to(-7, 0)\).
