Testinar Grade 8 math

Transformations on the Coordinate Plane

Learn to reason about and solve Grade 8 problems involving Transformations on the Coordinate Plane.

CH05-03 Geometry and Measurement

Name
Date
Score: ____ / 8

Directions Solve each problem. Show your reasoning on the page or on separate paper. Check the answer key only after finishing.

The blue triangle is the pre-image and the red triangle is the image. Which transformation maps the blue triangle to the red triangle?
1. Reflection across the \(x\)-axis
2. Translation left 2, down 2
3. Rotation 180° about the origin
4. Dilation by scale factor \(2\)
The blue square is the pre-image \(PQRS\) with \(P\) at \((0,1)\). The purple square is the image \(P'Q'R'S'\). What is the translation rule?
1. \((x,y)\to(x+1,y+3)\)
2. \((x,y)\to(x-1,y-3)\)
3. \((x,y)\to(x+2,y+2)\)
4. \((x,y)\to(x+3,y+1)\)
The blue rectangle is reflected to produce the red image. Over which line is the rectangle reflected?
1. The \(x\)-axis
2. The \(y\)-axis
3. The line \(y=x\)
4. The line \(y=-x\)
Shape \(X\) (brown) is rotated 90° counterclockwise about the origin to produce \(X'\) (pink). Which vertex of \(X'\) corresponds to the vertex at \((2,1)\) in \(X\)?
1. \((-1,2)\)
2. \((-2,1)\)
3. \((1,-2)\)
4. \((-3,1)\)
The blue rectangle is dilated to form the red rectangle. What is the scale factor?
1. \(\frac{1}{2}\)
2. \(2\)
3. \(\frac{1}{3}\)
4. \(3\)
Segment \(AB\) with endpoints \(A(2,1)\) and \(B(2,3)\) is rotated 90° counterclockwise about the origin. Which of the following is an endpoint of the image segment \(A'B'\)?
1. \((-1,2)\)
2. \((1,2)\)
3. \((3,2)\)
4. \((-2,2)\)
The red rectangle (pre-image) is transformed to the blue rectangle (image). Which sequence of transformations applies?
1. Reflect across \(x\)-axis, then translate right 1 and up 1
2. Translate right 1 and up 1, then reflect across \(x\)-axis
3. Reflect across the line \(y=x\)
4. Rotate 180°, translate right 3
Segment \(\ell\) (red) is reflected across the \(y\)-axis to produce \(\ell'\) (blue). If the length of \(\ell\) is 2 units, what is the length of \(\ell'\)?
1. \(1\) unit
2. \(2\) units
3. \(4\) units
4. \(\sqrt{2}\) units

Teacher and parent reference

Answer key and explanations

C. Rotation 180° about the origin
Under 180° rotation, \((x,y)\to(-x,-y)\): \((1,1)\to(-1,-1)\), \((3,1)\to(-3,-1)\), \((2,3)\to(-2,-3)\). This matches the red triangle.
A. \((x,y)\to(x+1,y+3)\)
\(P(0,1)\to P'(1,4)\) means the translation is right 1 and up 3: \((x,y)\to(x+1,y+3)\).
B. The \(y\)-axis
The pre-image \((1,2)\) maps to image \((-1,2)\), confirming reflection across the \(y\)-axis: \((x,y)\to(-x,y)\).
A. \((-1,2)\)
Under 90° counterclockwise rotation, \((x,y)\to(-y,x)\). So \((2,1)\to(-1,2)\).
A. \(\frac{1}{2}\)
The blue rectangle has width 3; the red has width \(1.5\). Scale factor is \(\frac{1.5}{3}=\frac{1}{2}\).
A. \((-1,2)\)
Rotation rule: \((x,y)\to(-y,x)\). So \(A(2,1)\to A'(-1,2)\).
A. Reflect across \(x\)-axis, then translate right 1 and up 1
Reflecting across the \(x\)-axis maps \((1,2)\to(1,-2)\). Translating right 1 and up 1 gives \((2,-1)\), which is a vertex of the image. Checking the other vertices shows the same rule maps the whole rectangle correctly.
B. \(2\) units
Reflections preserve distance. So \(\ell'\) has the same length as \(\ell\): 2 units.