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

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. Method of L.C.M. | Finding L.C.M. | Smallest Common Multiple | Common

    Apr 15, 24 01:29 AM

    LCM of 24 and 30
    We will discuss here about the method of l.c.m. (least common multiple). Let us consider the numbers 8, 12 and 16. Multiples of 8 are → 8, 16, 24, 32, 40, 48, 56, 64, 72, 80, 88, 96, ......

    Read More

  2. Common Multiples | How to Find Common Multiples of Two Numbers?

    Apr 15, 24 01:13 AM

    Common multiples of two or more given numbers are the numbers which can exactly be divided by each of the given numbers. Consider the following. (i) Multiples of 3 are: 3, 6, 9, 12, 15, 18, 21, 24…

    Read More

  3. Least Common Multiple |Lowest Common Multiple|Smallest Common Multiple

    Apr 14, 24 03:06 PM

    Lowest Common Multiple
    The least common multiple (L.C.M.) of two or more numbers is the smallest number which can be exactly divided by each of the given number. The lowest common multiple or LCM of two or more numbers is t…

    Read More

  4. Worksheet on H.C.F. | Word Problems on H.C.F. | H.C.F. Worksheet | Ans

    Apr 14, 24 02:23 PM

    HCF Using Venn Diagram
    Practice the questions given in the worksheet on hcf (highest common factor) by factorization method, prime factorization method and division method. Find the common factors of the following numbers…

    Read More

  5. Common Factors | Find the Common Factor | Worksheet | Answer

    Apr 14, 24 02:01 PM

    Common Factors of 24 and 36
    Common factors of two or more numbers are a number which divides each of the given numbers exactly. For examples 1. Find the common factor of 6 and 8. Factor of 6 = 1, 2, 3 and 6. Factor

    Read More