+91-705-589-3577
FlagBACK
Flag 10 grade maths> Find the coorddinates of the point of int...
question mark

Find the coorddinates of the point of intersection of the straight lines 2x-3y=1 and 5y-x=3 and determine the angle between them

samaira , 6 Years ago
Grade 10
anser 3 Answers
Aditya Gupta
to find the point of intersection simply solve the two eqns together. 2x-3y=1 and 5y-x=3 gives x= 2 and y= 1.
so coordinates of the point of intersection= (2, 1)
now, the formula for angle between 2 lines is 
theta= arctan[|(m1 – m2)/(1+m1*m2)|], where m1 and m2 are the slopes of the lines.
here, m1= 2/3 for 2x-3y=1 and m2= 1/5 for 5y-x=3.
so, theta= arctan[|(m1 – m2)/(1+m1*m2)|]= arctan(7/17) which is approx 22.38 degrees.
kindly approve :)
Last Activity: 6 Years ago
Vikas TU
Dear student 
in equation 1 , a1 = 2 , b1 = -3 , 
in equation 2 a2 = 5 , b2 = -1 
a1/a2 is not equal to b1 / b2 
so, this is the condition of line to intersect , 
and angle between them = 22.38 degree.
Last Activity: 6 Years ago
Pawan Kumar Karela
Given equation    2x-3y=1   (1)
                            5y-x=3     (2)
we use the elimination method to get the intersection point.
therefore multiply equation (2) by 2 and then add it to equation (1) to eliminate variable y.
                          2x-3y=1     (3)
                         -2x+10y=6  (4)
adding (3) and (4) we get 
                            7y=7
                           y=1      (*)
              use value of y to get x
                     2x-3*1=1
                        2x=1+3
                         x=2
         therefore point of intersection is (2,1)
 
to find angle between these two lines we use formula
                                  tan\Theta =\left | \frac{m1-m2}{1+m1*m2} \right |
from equation (1)  2x-3y=1...... implies y=(2/3)x-1
                                                      therefore m1=2/3
similarly for equation (2)  y=1/5+3/5
                                       therefore m2=1/5
               hence tan\Theta =\left | \frac{(2/3)-(1/5)}{1+(2/3)*(1/5)} \right |
                           therefore on solving we get
                                      tan\Theta =\left | \frac{7}{17}\right |
                                       \Theta =tan^-1\left | \frac{7}{17}\right |
Last Activity: 6 Years ago
star
LIVE ONLINE CLASSES

Prepraring for the competition made easy just by live online class.

tv

Full Live Access

material

Study Material

removal

Live Doubts Solving

assignment

Daily Class Assignments


Other Related Questions on 10 grade maths

question mark

How do you find the Maclaurin series for tanx?

10 grade maths
1 Answer Available

Last Activity: 7 Months ago

question mark

Why is Axiom 5, in the list of Euclid’s axioms, considered a ‘universal truth’? (Note that the equation is not about the fifth postulate.)

10 grade maths
1 Answer Available

Last Activity: 7 Months ago

question mark

The smallest composite number is ______.

(a) 2

(b) 4

(c) 1

(d) None of these

10 grade maths
1 Answer Available

Last Activity: 7 Months ago

question mark

Find the arithmetic mean of the first ten odd natural numbers.

10 grade maths
1 Answer Available

Last Activity: 7 Months ago

question mark

A boat goes 24 km upstream and 28 km downstream in 6 hours. It goes 30 km upstream and 21 km downstream in 6 hours and 30 minutes. The speed of the boat in still water is

A. 10 km/hr

B. 4 km/hr

C. 14 km/hr

D. 6 km/hr

10 grade maths
1 Answer Available

Last Activity: 7 Months ago