**Finding a scale factor :**

A dilation can produce a larger figure (an enlargement) or a smaller figure (a reduction). The scale factor describes how much the figure is enlarged or reduced. The scale factor is the ratio of a length of the image to the corresponding length on the original figure.

**Example 1 :**

An art supply store sells several sizes of drawing triangles. All are dilations of a single basic triangle. The basic triangle and one of its dilations are shown on the grid. Find the scale factor of the dilation.

**Solution :**

**Step 1 :**

Use the coordinates to find the lengths of the sides of each triangle.

Triangle PQR :

PR = 2, RQ = 3

Triangle P'Q'R' :

P'R' = 4, R'Q' = 6

**Step 2 :**

Find the ratios of the corresponding sides.

P'R'/PR = 4/2 = 2

R'Q'/RQ = 6/3 = 2

Hence, the scale factor of the dilation is 2.

**Example 2 :**

Find the scale factor of the dilation.

**Solution : **

**Step 1 : **

Use the coordinates to find the lengths of the sides of each triangle.

Since the scale factor is the same for all corresponding sides, we can record just two pairs of side lengths. Use one pair as a check on the other.

Rectangle ABCD :

AB = 6, AD = 4

Rectangle A'B'C'D' :

A'B' = 3, A'D' = 2

**Step 2 :**

Find the ratios of the corresponding sides.

A'B'/AB = 3/6 = 0.5

A'D'/AD = 2/4 = 0.5

Hence, the scale factor of the dilation is 0.5

**Example 3 :**

Find the scale factor of the dilation.

**Solution :**

**Step 1 :**

Use the coordinates to find the lengths of the sides of each triangle.

Since the scale factor is the same for all corresponding sides, we can record just a pair of side lengths. Use one pair as a check on the other.

Since the sides of the triangle and its image after dilation are not parallel to x and y axes, we can use the distance between two points formula to find the lengths of the sides.

Triangle ABC :

AB = √17, AC = √17

Triangle A'B'C' :

A'B' = √68, A'C' = √68

**Step 2 :**

Find the ratios of the corresponding sides.

A'B'/AB = √68/√17 = √4 = 2

A'C'/AC = √68/√17 = √4 = 2

Hence, the scale factor of the dilation is 2.

After having gone through the stuff given above, we hope that the students would have understood "Dilations".

Apart from the stuff given above, if you want to know more about "Finding a scale factor", please click here

Apart from the stuff given in this section, if you need any other stuff in math, please use our google custom search here.

HTML Comment Box is loading comments...

**WORD PROBLEMS**

**HCF and LCM word problems**

**Word problems on simple equations **

**Word problems on linear equations **

**Word problems on quadratic equations**

**Area and perimeter word problems**

**Word problems on direct variation and inverse variation **

**Word problems on comparing rates**

**Converting customary units word problems **

**Converting metric units word problems**

**Word problems on simple interest**

**Word problems on compound interest**

**Word problems on types of angles **

**Complementary and supplementary angles word problems**

**Markup and markdown word problems **

**Word problems on mixed fractrions**

**One step equation word problems**

**Linear inequalities word problems**

**Ratio and proportion word problems**

**Word problems on sets and venn diagrams**

**Pythagorean theorem word problems**

**Percent of a number word problems**

**Word problems on constant speed**

**Word problems on average speed **

**Word problems on sum of the angles of a triangle is 180 degree**

**OTHER TOPICS **

**Time, speed and distance shortcuts**

**Ratio and proportion shortcuts**

**Domain and range of rational functions**

**Domain and range of rational functions with holes**

**Graphing rational functions with holes**

**Converting repeating decimals in to fractions**

**Decimal representation of rational numbers**

**Finding square root using long division**

**L.C.M method to solve time and work problems**

**Translating the word problems in to algebraic expressions**

**Remainder when 2 power 256 is divided by 17**

**Remainder when 17 power 23 is divided by 16**

**Sum of all three digit numbers divisible by 6**

**Sum of all three digit numbers divisible by 7**

**Sum of all three digit numbers divisible by 8**

**Sum of all three digit numbers formed using 1, 3, 4**

**Sum of all three four digit numbers formed with non zero digits**