We can perform transformations on a coordinate plane by changing the coordinates of the points on a figure. The points on the translated figure are indicated by the prime "symbol" to distinguish them from the original points

Reflection |
A point on a coordinate plane can be reflected across an axis. The reflection is located on the opposite side of the axis, at the same distance from the axis. | |

Translation |
A translation "slides" an object a fixed distance in a given direction. The original object and its translation have the same shape and size, and they face in the same direction. It is a direct isometry. | |

Dilation |
A dilation is a transformation that produces an image that is the same shape as the original, but is a different size. NOT an isometry. Forms similar figures. | |

Rotation |
To rotate a figure 90 degree clockwise about the origin, switch the coordinates of each point and then multiply the new first coordinate by -1. To rotate 180 degree about origin, multiply both coordinates of each point by -1. |

**Example 1 :**

Graph (3, −2). Then fold your coordinate plane along the y-axis and find the reflection of (3, −2). Record the coordinates of the new point in the table.

**Solution :**

**Example 2 :**

Graph (3, −2). Then fold your coordinate plane along the x-axis and find the reflection of (3, −2). Record the coordinates of the new point in the table.

**Solution :**

Once students understand the rules which they have to apply for reflection transformation, they can easily make reflection -transformation of a figure.

For example, if we are going to make reflection transformation of the point (2,3) about x-axis, after transformation, the point would be (2,-3). Here the rule we have applied is (x, y) ------> (x, -y).

So we get (2,3) -------> (2,-3).

Translation of (h, k) :

**(x, y) -----> (x + h, y + k)**

**Example 3 :**

Let A ( -2, 1), B (2, 4) and (4, 2) be the three vertices of a triangle. If this triangle is translated for ( h, k ) = ( 2, 3) what will be the new vertices A' , B' and C' ?

**Solution :**

**Step 1 :**

First we have to know the correct rule that we have to apply in this problem.

**Step 2 :**

Here triangle is translated for (h , k ) = ( 2 , 3 ).

So the rule that we have to apply here is

(x, y) -------> (x + h, y + k)

**Step 3 :**

Based on the rule given in step 1, we have to find the vertices of the translated triangle A'B'C'

**Step 4 :**

**(x , y) -----> (x + h, y + k)**

A(-2, 1) -------> A'(0, 4)

B(2, 4) -------> B'(4, 7)

C(4, 2) -------> C'(6, 5)

**Step 5 :**

Vertices of the translated triangle are

A'(0, 4), B(4, 7) and C'(6, 5)

Dilation of scale factor **"k" : **

**(x, y) -----> (kx, ky)**

Dilation for "k = 2".

**Example 4 : **

Let A(-2, -2), B(-1, 2) and C(2, 1) be the three vertices of a triangle. If this triangle is dilated for the scale factor "k = 2", what will be the new vertices A', B' and C' ?

**Solution:**

**Step 1 :**

First we have to know the correct rule that we have to apply in this problem.

**Step 2 :**

Here, triangle is dilated for the scale factor "k = 2".

So, the rule that we have to apply here is

(x, y) -------> (kx , ky)

**Step 3 :**

Based on the rule given in step 1, we have to find the vertices of the dilated triangle A'B'C'

**Step 4 :**

**(x, y) -----> (kx, ky)**

A(-2, -2) -------> A'(-4, -4)

B(-1, 2) -------> B'(-2, 4)

C(2, 1) -------> C'(4, 2)

**Step 5 :**

Vertices of the dilated triangle are

A'(-4, -4), B(-2, 4) and C'(4, 2)

**Example 5 :**

Let A(-2, 1), B(2, 4) and C(4, 2) be the three vertices of a triangle. If this triangle is rotated about 90° clockwise, what will be the new vertices A', B' and C' ?

**Solution :**

**Step 1 :**

First we have to know the correct rule that we have to apply in this problem.

**Step 2 :**

Here triangle is rotated about 90° clock wise. So the rule that we have to apply here is

(x, y) -------> (y, -x)

**Step 3 :**

Based on the rule given in step 1, we have to find the vertices of the reflected triangle A'B'C'.

**Step 4 :**

**(x, y) -----> (y, -x)**

A(-2, 1) -------> A'(1, 2)

B(2, 4) -------> B'(4, -2)

C(4, 2) -------> C'(2, -4)

**Step 5 :**

Vertices of the reflected triangle are

A'(1, 2), B(4, -2) and C'(2, -4)

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

HTML Comment Box is loading comments...

You can also visit the following web pages on different stuff in math.

**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**

**Trigonometry 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**