**Find the Equation of the Line in the New Position :**

Here we are going to see how to find the equation of the line in the new position if a line joining two points is rotated about the point in counter clockwise direction through given angle.

**Question 1 :**

If the line joining two points A(2,0) and B(3,1) is rotated about A in anticlockwise direction through an angle of 15°, then find the equation of the line in new position.

**Solution :**

Let us represent the given information in a picture.

Let A (2, 0) and B (3, 1) be the given points.

Slope of PQ = (y_{2} − y_{1}) / (x_{2} − x_{1})

= (1 - 0) / (3 - 2)

= 1 ⇒ the angle of inclination of

the line AB = tan−1(1) = π/4 = 45^{◦}

The slope of the line in new position is

m = tan(45^{◦} + 15^{◦})

Slope = tan(60^{◦}) = (√3)

Equation of the straight line passing through (2, 0) and with the slope √3 is

y − 0 = 2 (x − √3)

2x − y + 2√3 = 0

**Question 2 :**

A ray of light coming from the point (1, 2) is reflected at a point A on the x-axis and it passes through the point (5,3). Find the co-ordinates of the point A.

**Solution :**

Let us represent the given details in a rough diagram.

The reflection point of A is A'. Its coordinate will be (1, -2).

Equation of A'B :

A'(1, -2) B (5, 3)

(y - y_{1}) / (y_{2} - y_{1}) = (x - x_{1})/(x_{2} - x_{1})

(y - 3) / (3 + 2) = (x - 5)/(5 - 1)

(y - 3) / 5 = (x - 5)/4

4 (y - 3) = 5 (x - 5)

4y - 12 = 5x - 25

5x - 4y - 25 + 12 = 0

5x - 4y - 13 = 0

The required point (x, 0) lies on the line A'B

5x - 4(0) - 13 = 0

5x - 13 = 0

5x = 13

x = 13/5

Hence the required point is (13/5, 0).

After having gone through the stuff given above, we hope that the students would have understood "Find the Equation of the Line in the New Position".

Apart from the stuff given above, if you want to know more about "Find the Equation of the Line in the New Position".

If you have any feedback about our math content, please mail us :

**v4formath@gmail.com**

We always appreciate your feedback.

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**