Reduction Transformation

We will discuss here about the similarity on Reduction transformation.

In the figure given below ∆X’Y’Z’ is a reduced image of ∆XYZ. 

Reduction Transformation

The two triangles are similar. Here also the triangles are equiangular and \(\frac{X’Y’}{XY}\) = \(\frac{Y’Z’}{YZ}\) = \(\frac{Z’X’}{ZX}\) = k.

Here k is known as the reduction factor and P is known as the centre of reduction.

Therefore, in a size transformation, a given figure undergoes enlargement or reduction by a scale factor k, such that the resulting figure is similar to the original figure, i.e., the image retains the shape of the original object.

Reduction Scale Factor

If ∆XYZ is transformed to ∆X’Y’Z’ by a scale factor k about the point P, we get \(\frac{PX’}{PX}\) = \(\frac{PY’}{PY}\) = \(\frac{PZ’}{PZ}\) = k.

2. A rectangle PQRS has been reduced to a rectangle P’ Q’ R’ S’ and their areas are 192 cm\(^{2}\) and 12 cm\(^{2}\) respectively. If Q’ R’ is 3 cm, then find QR.


Let \(\frac{area of P’ Q’ R’ S’}{area of PQRS}\) = k\(^{2}\)

Therefore, \(\frac{12 cm\(^{2}\)}{192 cm\(^{2}\)}\) = k\(^{2}\)

⟹ \(\frac{1}{16}\) k\(^{2}\)

⟹ k = \(\frac{1}{4}\)

Now, \(\frac{Q’ R’}{QR}\) = k

⟹ \(\frac{3 cm}{QR}\) = \(\frac{1}{4}\)

⟹ QR = 12 cm

9th Grade Math

From Reduction Transformation to HOME PAGE

New! Comments

Have your say about what you just read! Leave me a comment in the box below. Ask a Question or Answer a Question.

Didn't find what you were looking for? Or want to know more information about Math Only Math. Use this Google Search to find what you need.

Share this page: What’s this?

Recent Articles

  1. 2nd grade math Worksheets | Free Math Worksheets | By Grade and Topic

    Dec 06, 23 01:23 AM

    2nd Grade Math Worksheet
    2nd grade math worksheets is carefully planned and thoughtfully presented on mathematics for the students.

    Read More

  2. Rupees and Paise | Paise Coins | Rupee Coins | Rupee Notes

    Dec 04, 23 02:14 PM

    Different types of Indian Coins
    Money consists of rupees and paise; we require money to purchase things. 100 paise make one rupee. List of paise and rupees in the shape of coins and notes:

    Read More

  3. Months of the Year | List of 12 Months of the Year |Jan, Feb, Mar, Apr

    Dec 04, 23 01:50 PM

    Months of the Year
    There are 12 months in a year. The months are January, February, march, April, May, June, July, August, September, October, November and December. The year begins with the January month. December is t…

    Read More