**Perpendicular lines worksheet :**

Perpendicular lines worksheet is much useful to the students who would like to practice problems on coordinate geometry.

If you want to know some basic stuff about perpendicular lines, please click here.

1) The slopes of the two lines are 7 and (3k +2). If the two lines are perpendicular, find the value of "k"

2) The equations of the two perpendicular lines are

3x + 2y - 8 = 0

(5k+3) - 3y + 1 = 0

Find the value of "k"

3) Find the equation of a straight line is passing through (2, 3) and perpendicular to the line 2x - y + 7 = 0.

4) Verify, whether the two lines 3x - 2y - 7 = 0 and y = - (2x/3) + 4 are perpendicular.

5) Verify, whether the two lines 5x + 7y - 1 = 0 and 14x - 10y + 5 = 0 are perpendicular.

**Problem 1 :**

The slopes of the two lines are 7 and (3k +2). If the two lines are perpendicular, find the value of "k"

**Solution :**

If the given two lines are parallel, then the product of the slopes is equal to -1.

7(3k + 2) = - 1

21k + 14 = -1

21k = -15

k = -15/21

**k = -5/7**

**Problem 2 :**

The equations of the two perpendicular lines are

3x + 2y - 8 = 0

(5k+3) - 3y + 1 = 0

Find the value of "k"

**Solution :**

If the two lines are perpendicular, then the coefficient "y" term in the first line is equal to the coefficient of "x" term in the second line.

So, we have

5k + 3 = 2

5k = -1

**k = -1/5**

**Problem 3 :**

Find the equation of a straight line is passing through (2, 3) and perpendicular to the line 2x - y + 7 = 0.

**Solution :**

Since the required line is perpendicular to 2x - y + 7 = 0,

then, equation of the required line is x + 2y + k = 0 ------> (1)

The required line is passing through (2, 3).

So, we can plug x = 2 and y = 3 in the equation of the required line.

2 + 2(3) + k = 0

2 + 6 + k = 0

8 + k = 0

k = - 8

**Hence, the equation of the required line is x + 2y - 8 = 0.**

**Problem 4 :**

Verify, whether the two lines 3x - 2y - 7 = 0 and y = - (2x/3) + 4 are perpendicular.

**Solution :**

In the equations of the given two lines, the equation of the second line is not in general form.

Let us write the equation of the second line in general form.

y = - (2x/3) + 4

Multiply by 3 on both sides,

3y = - 2x + 12

2x + 3y - 12 = 0

Now, let us compare the equations of two lines,

3x - 2y - 7 = 0

2x + 3y - 12 = 0

When we look at the general form of equations of the above two lines, we get the following points.

(i) The sign of y- terms are different.

(ii) The coefficient of "x" term in the first equation is the coefficient of "y" term in the second equation.

(iii) The coefficient of "y" term in the first equation is the coefficient of "x" term in the second equation.

(iv) The above equations differ in constant terms.

Considering the above points, it is clear that the given two lines are perpendicular.

**Hence, the equations of the given two lines are perpendicular.**

**Problem 5 :**

Verify, whether the two lines 5x + 7y - 1 = 0 and 14x - 10y + 5 = 0 are perpendicular.

**Solution :**

In the equation of the second line 14x-10y + 5 = 0, the coefficients of "x" and "y" have the common divisor 2.

So, let us divide the second equation by 2

(14x/2) - (10y/2) + (5/2) = (0/2)

7x - 5y + 2.5 = 0

Now, let us compare the equations of two lines,

5x + 7y - 1 = 0

7x - 5y + 2.5 = 0

When we look at the general form of equations of the above two lines, we get the following points.

(i) The sign of y- terms are different.

(ii) The coefficient of "x" term in the first equation is the coefficient of "y" term in the second equation.

(iii) The coefficient of "y" term in the first equation is the coefficient of "x" term in the second equation.

(iv) The above equations differ in constant terms.

Considering the above points, it is clear that the given two lines are perpendicular.

**Hence, the equations of the given two lines are perpendicular.**

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

Apart from the stuff given above, if you want to know more about "Perpendicular lines worksheet", please click here

Apart from the stuff, "Perpendicular lines worksheet", 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**