← Pre-Algebra

Unit 13: Transformations, Similarity, and Scale

Sliding, flipping, and turning a shape without changing it, and what happens when a shape grows while its angles stay put.

4 topics · 13 questions

Each topic is a path, not a menu: work down it in order and every question builds on the one above. Click any of them to watch the answer draw itself.

Translations, Reflections, and Rotations

  1. How it worksHow do a translation, a reflection, and a rotation each move every point of a shape by the same consistent rule?
  2. Worked exampleFind the new coordinates after reflecting the triangle with vertices 1 comma 2, 3 comma 2, and 3 comma 5 across the y-axis.
  3. Common mistakeWhy doesn't rotating a shape 180 degrees give the same result as reflecting it?
Your turn1 of 2
A game piece sits at x equals 14 on a grid and is reflected across the y-axis. What is its new x-coordinate?

Congruence and Rigid Transformations

  1. How it worksHow does a sequence of translations, reflections, and rotations prove two figures are congruent?
  2. Worked exampleExplain a sequence of transformations that maps triangle A onto triangle B, given that B is A rotated 90 degrees and shifted 3 units right.
  3. Common mistakeWhy doesn't stretching a shape bigger while keeping its angles the same count as a rigid transformation?
Your turn1 of 2
Triangle B is triangle A rotated 202 degrees and shifted 7 units to the right. Are triangles A and B congruent?

Dilations and Similarity

  1. How it worksHow does a scale factor stretch or shrink every distance from a center point while every angle stays locked in place?
  2. Worked exampleFind the coordinates of the point 4 comma 6 after a dilation with scale factor 0.5 centered at the origin.
  3. Common mistakeWhy doesn't dilating a shape by a scale factor of 2 double its area instead of quadrupling it?
  4. Going furtherWhat happens to a shape's angles and side lengths when the scale factor is less than 1?
Your turn1 of 2
A logo design has a corner point at (14, 13), and the whole design is scaled by a factor of 2.83 from the origin. What is the new x-coordinate of that corner?

Scale Drawings

  1. How it worksHow does a scale like 1 inch equals 4 feet convert every measurement on a drawing into a real-world length?
  2. Worked exampleFind the actual length of a wall that measures 3.5 inches on a blueprint with a scale of 1 inch equals 4 feet.
  3. Ties togetherHow does a scale drawing use the exact same idea as a dilation, just applied to an entire floor plan?
Your turn1 of 2
An architect's blueprint uses a scale of 1 inch equals 8 feet. If a wall measures 8 inches on the blueprint, what is its actual length?