**Exploring translations :**

Function is a rule that assigns exactly one output to each input. A transformation is a function that describes a change in the position, size, or shape of a figure. The input of a transformation is the pre-image, and the output of a transformation is the image.

The triangle PQR has the following vertices.

P(1, 11), Q(1, 7) and R(3, 7).

(i) Trace triangle PQR and line PP′ onto a piece of paper as given below.

(ii) Slide your triangle along the line to model the translation that maps point P to point P′.

(iii) The image of the translation is the triangle produced by the translation.

Sketch the image of the translation.

(iv) The vertices of the image are labeled using prime notation. For example, the image of P is P′. Label the images of points Q and R.

(v) Describe the motion modeled by the translation.

Move **7 units **to the right and** 5 units** down.

(vi) Check that the motion we described in part (v) is the same motion that maps point Q onto Q′.

Is the orientation of the triangle affected by the translation ?

No

The orientation of the triangle is not affected and it stays the same.

**Example 1 : **

A triangle has the vertices P (-6, 2), Q(-7, -5) and R(-2, -3). P', Q'and R' are the vertices of the triangle after a translation of 7 units to the right and 2 units up. Find the vertices P', Q' and R'

**Solution : **

Since there is a translation of 7 units to the right and 2 units up, we have to add 7 to x-coordinate and add 2 to y-coordinate of each vertex.

P' ------> (-6+7, 2+2) = (1, 4)

Q' ------> (-7+7, -5+2) = (0, -3)

R' ------> (-2+7, -3+2) = (5, -1)

**Example 2 :**

A trapezoid has the vertices A (1, 0), B(4, 0), C(4, -4) and D(0, -4). A', B', C'and D' are the vertices of the trapezoid after a translation of 5 units to the left and 3 units up. Find the vertices A', B', C' and D'

**Solution : **

Since there is a translation of 5 units to the left and 3 units up , we have to subtract 5 from x-coordinate and add 3 to y-coordinate of each vertex.

A' ------> (1-5, 0+3) = (-4, 3)

B' ------> (4-5, 0+3) = (-1, 3)

C' ------> (4-5, -4+3) = (-1, -1)

D' ------> (0-5, -4+3) = (-5, -1)

After having gone through the stuff given above, we hope that the students would have understood "How to translate a figure".

Apart from the stuff given above, if you want to know more about "Translations", 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**