# Important Questions for Class 11 Chapter 10 - Straight lines

The Important Questions we provided is a good collection of varieties of questions that help the student of class 11 to practice a lot. Practice makes you better. Practice well and get good score.

**Important questions based on NCERT syllabus for Class 11 Chapter 10 - Straight lines:**

*Question 1*:Find the point on the x-axis which is equidistant from the points (3,8) and (5,9)

*Solution*: Let the point on the x-axis be P(x,0)

Let A = (3,8) and B = (5,9)

Now PA = √(x-3)^2 + (0-8)^2

PA = √(x-3)^2 + 64

PA^2 = (x-3)^2 + 64

And PB = √(x-5)^2 + (0-9)^2

PB = √(x-5)^2 + 81

PB^2 = (x-5)^2 + 81

Given PA = PB or PA^2 = PB^2

or (x-3)^2 + 64 = (x-5)^2 + 81

or x^2 + 9 - 6x + 64 = x^2 + 25 - 10x + 81

o -6x + 73 = -10x + 106

or -6x + 10x = 106 - 73

or 4x = 33

or x = 33/4

Hence the required point is (33/4, 0)

*Question 2*: The line passes through the origin and mid point of the line sengment. find the slope of the line whose point are A(0, 7) and B(5, 0)

*Solution*: Let the ,id point of the A(0, 6) and B(10, 0) be C

Therefore, C = [(0+10)/2 , (6+0)/2] = [5, 3]

Origin is o[0,0]

Slope of OC = (y_2 - y_1)/(x_2- x_1) = 0-3/0-5 = -3/-5 = 3/5

Hence the slope of the line = 3/5

*Question 3*: Find the equation of the diagonal of the quadrilateral whose vertice are (2,3)(4,6)(7,3) and (9,1)

*Solution*:

Let P(2,3) Q(4,6) R(7,8) and S(9,1) be the vertices of the quadrilateral PQRS

Equation of the diagonal PR = (y - 3)/(3-8) = (x- 2)/(2-7)

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

=> (y - 3) = (x- 2)

=> y - x -3 + 2 = 0

=> y - x - 1 = 0

Equation of the diagonal QS = (y-6)/6 - 1 = (x - 4)/4 - 9)

=(y - 6)/5 = (x - 4)/-5

=> -(y - 6) = (x - 4)

=> -y + 6 = x - 4

=> -y -x + 6 + 4 = 0

=> y + x - 10 = 0