Dilate a Triangle by a Scale Factor of 0.5

✏️ Worked Example

Dilate Triangle \(ABC\) by a Scale Factor of \(0.5\)

The center of dilation is the origin, so use the coordinate rule:

\((x,y)\rightarrow(kx,ky)\)

Here, the scale factor is \(k=0.5\), so multiply every coordinate by \(0.5\).

\(A(-4,-5)\rightarrow A'(-2,-2.5)\)
\(B(-1,5)\rightarrow B'(-0.5,2.5)\)
\(C(4,-5)\rightarrow C'(2,-2.5)\)

What to notice:
Each image point is halfway from the origin to its matching preimage point. Since \(0.5<1\), the triangle shrinks.

The image triangle is similar to the original triangle, but smaller. This is a non-rigid transformation because the size changes.

🧠 Math Vocabulary

• Dilation: a transformation that changes the size of a figure while keeping the same shape.
• Scale Factor: the number \(k\) used to enlarge or reduce a figure.
• Fractional Scale Factor: a scale factor between \(0\) and \(1\), which creates a reduction.
• Center of Dilation: the fixed point from which distances are scaled.
• Origin: the point \((0,0)\), used as the center of dilation in this lesson.
• Image: the new figure after the transformation.
• Preimage: the original figure before the transformation.
• Non-Rigid Transformation: a transformation that changes the size of a figure.

📚 What You Should Already Know

Students should know how to plot ordered pairs, multiply decimals and fractions, identify the origin, and understand that \(0.5=\frac{1}{2}\).

🚀 What Comes Next

Next, students can compare fractional scale factors with scale factors greater than \(1\), and practice dilations when the center of dilation is not the origin.

🧩 Embed This Video in Your LMS

Teachers can embed this YouTube Short directly into Canvas, Google Classroom, Schoology, or another learning platform. Click below to show the embed code.