Processing math: 100%

Word Problems on Straight Lines

Here we will solve different types of word problems on straight lines.

1.Find the equation of a straight line that has y-intercept 4 and is perpendicular to straight line joining (2, -3) and (4, 2).

Solution:

Let m be the slope of the required straight line.

Since the required straight line is perpendicular to the line joining P (2, -3) and Q (4, 2).

Therefore,

m × Slope of PQ = -1

⇒ m ×  2+342 = -1

⇒ m ×  52 = -1

⇒ m = -25

The required straight lien cut off an intercept of length 4 on y-axis.

Therefore, b = 4

Hence, the equation of the required straight line is y = -25x + 4

⇒ 2x + 5y - 20 = 0

 

2. Find the co-ordinates of, the middle point of the portion of the line 5x + y = 10 intercepted between the x and y-axes.

Solution:    

The intercept form of the given equation of the straight line is,

5x + y = 10

Now dividing both sides by 10 we get,

5x10+ y10 = 1        

x2 + y10 = 1.

Therefore, it is evident that the given straight line intersects the x-axis at P (2, 0) and the y-axis at Q (0, 10).

Therefore, the required co-ordinates of the middle point of the portion of the given line intercepted between the co-ordinate axes = the co-ordinates of the middle point of the line-segment PQ

= (2+02, 0+102)

= (22, 102)

= (1, 5)


More examples on word problems on straight lines.

3. Find the area of the triangle formed by the axes of co-ordinates and the straight line 5x + 7y = 35.

Solution:  

The given straight line is 5x + 7y = 35.

The intercept form of the given straight line is,

5x + 7y = 35

5x35+ 7y35 = 1, [Dividing both sides by 35]      

x7 + y5 = 1.

Therefore, it is evident that the given straight line intersects the x-axis at P (7, 0) and the y-axis at Q (0, 5).

Thus, if o be the origin then, OP = 7 and OQ = 5

Therefore, the area of the triangle formed by the axes of co-ordinates and the given line = area of the right-angled ∆OPQ

= ½ |OP × OQ|= ½ ∙ 7 . 5 = 352 square units.

 

4. Prove that the points (5, 1), (1, -1) and (11, 4) are collinear. Also find the equation of the straight line on which these points lie.

Solution:

Let the given points be P (5, 1), Q (1, -1) and R (11, 4). Then the equation of the line passing through P and Q is

y - 1 = 1115(x - 5)

⇒ y - 1 = 24(x - 5)

⇒ y - 1 = 12(x - 5)

⇒ 2(y - 1) = (x - 5)

⇒ 2y - 2 = x - 5

⇒ x - 2y - 3 = 0

Clearly, the point R (11, 4) satisfies the equation x - 2y - 3 = 0. Hence the given points lie on the same straight line, whose equation is x - 2y - 3 = 0.

 The Straight Line






11 and 12 Grade Math 

From Word Problems on Straight Lines to HOME PAGE




Didn't find what you were looking for? Or want to know more information about Math Only Math. Use this Google Search to find what you need.



New! Comments

Have your say about what you just read! Leave me a comment in the box below. Ask a Question or Answer a Question.




Share this page: What’s this?

Recent Articles

  1. Worksheet on Area of a Square and Rectangle | Area of Squares & Rectan

    Jul 19, 25 05:00 AM

    Area and Perimeter of Square and Rectangle
    We will practice the questions given in the worksheet on area of a square and rectangle. We know the amount of surface that a plane figure covers is called its area. 1. Find the area of the square len…

    Read More

  2. Area of Rectangle Square and Triangle | Formulas| Area of Plane Shapes

    Jul 18, 25 10:38 AM

    Area of a Square of Side 1 cm
    Area of a closed plane figure is the amount of surface enclosed within its boundary. Look at the given figures. The shaded region of each figure denotes its area. The standard unit, generally used for…

    Read More

  3. What is Area in Maths? | Units to find Area | Conversion Table of Area

    Jul 17, 25 01:06 AM

    Concept of Area
    The amount of surface that a plane figure covers is called its area. It’s unit is square centimeters or square meters etc. A rectangle, a square, a triangle and a circle are all examples of closed pla…

    Read More

  4. Worksheet on Perimeter | Perimeter of Squares and Rectangle | Answers

    Jul 17, 25 12:40 AM

    Most and Least Perimeter
    Practice the questions given in the worksheet on perimeter. The questions are based on finding the perimeter of the triangle, perimeter of the square, perimeter of rectangle and word problems. I. Find…

    Read More

  5. Formation of Square and Rectangle | Construction of Square & Rectangle

    Jul 16, 25 11:46 PM

    Construction of a Square
    In formation of square and rectangle we will learn how to construct square and rectangle. Construction of a Square: We follow the method given below. Step I: We draw a line segment AB of the required…

    Read More