Properties of Dilations
Aligned to G-SRT.A.1 — Common Core State Standards for Mathematics.
What this lesson teaches
A dilation with center O and scale factor k moves each point P to P' on ray OP so that OP' = k times OP. A dilation multiplies all distances by k but keeps every line parallel to its image, and it fixes the center. This is why dilated figures are similar, not congruent (unless k = 1).
Worked example
Dilate point A(2, 4) from the origin with scale factor 3. Multiply each coordinate by 3: A' = (3*2, 3*4) = (6, 12). The image lies on the ray from the origin through A, three times as far out. A segment from the origin to A is tripled in length, matching the scale factor.
Practice questions
- Dilate B(1, -2) from the origin with scale factor 4. Give B'.
- A dilation with center O and scale factor 1/2 is applied to a segment of length 10. Find the image length.
- A line does not pass through the center of a dilation. What is true about the line and its image?
Watch the lesson
Every lesson comes with a video taught in English and Spanish — the same video the QR code in the printed workbook opens.
▶ Watch this lessonEn español
Propiedades de las dilataciones
Una dilatación con centro O y factor de escala k mueve cada punto P a P' sobre el rayo OP de modo que OP' = k por OP. Una dilatación multiplica todas las distancias por k pero mantiene cada línea paralela a su imagen, y deja fijo el centro. Por eso las figuras dilatadas son semejantes, no congruentes (a menos que k = 1).
Ejemplo: Dilata el punto A(2, 4) desde el origen con factor de escala 3. Multiplica cada coordenada por 3: A' = (3*2, 3*4) = (6, 12). La imagen está sobre el rayo del origen que pasa por A, tres veces más lejos. Un segmento del origen a A se triplica, coincidiendo con el factor de escala.
More Similarity, Right Triangles & Trigonometry lessons
Teach this lesson today
An AI tutor that guides with questions instead of just giving answers — all K–12 core subjects, every child in the family.
Start free — no card required