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We will discuss here about the similarity on Reduction transformation.
In the figure given below ∆X’Y’Z’ is a reduced image of ∆XYZ.
The two triangles are similar. Here also the triangles are equiangular and X′Y′XY = Y′Z′YZ = 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.
If ∆XYZ is transformed to ∆X’Y’Z’ by a scale factor k about the point P, we get PX′PX = PY′PY = PZ′PZ = k.
2. A rectangle PQRS has been reduced to a rectangle P’ Q’ R’ S’ and their areas are 192 cm2 and 12 cm2 respectively. If Q’ R’ is 3 cm, then find QR.
Solution:
Let areaofP′Q′R′S′areaofPQRS = k2
Therefore, 12cm\(2\)192cm\(2\) = k2
⟹ 116 k2
⟹ k = 14
Now, Q′R′QR = k
⟹ 3cmQR = 14
⟹ QR = 12 cm
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