Test Questions list on Straight line

Question 21

Question:   Find the parametric form of a straight line.

Answer:   
In the figure, let AP = r



This is the parametric form of the straight line.

Question 22

Question:   Find the co-ordinates of the foot of the perpendicular from the point (3,-3) on the line 4x - 7y + 25 = 0.

Answer:   
This line passes through (3, -3).

The line is 7x + 4y = 9 -(ii)
Solving (i) and (ii), we get

Question 23

Question:  

Answer:    Equation of the line through (2,-1) with slope m is

Slope of given line is -1.

Question 24

Question:   Find the coordinates of the points A (7,4), B (-3,6) which divides the line segment joining the points A and B in the ratio 3:2
i) internally and
ii) externally.

Answer:    x₁ = 7, x₂ = -3
y₁ = 4, y₂ = 6
m = 3, n = 2

i) Internal division:







ii) External division:



x = -23, y = 10
\ The required point is (-23,10).

Question 25

Question:   Find the coordinates of the points A(-3,-4), B(-8,7) which divides the line segment joining the points A and B in the ratio 7:5
i) internally and
ii) externally.

Answer:    x₁ = -3, x₂ = -8
y₁ = -4, y₂ = 7
m = 7, n = 5

i)Internal division:






ii) External division:

Question 26

Question:   What are the co-ordinates of the point which trisect the line segment joining the points (1,2) and (11,9)?

Answer:   
Let C and D trisect the line segment AB. C divides AB in the ratio AC:CB::1:2.
Co-ordinates of C are



Co-ordinates of D are

Question 27

Question:   A (4,5) and B (1, -7) are two points and C is a point on AB produced such that AC = 4AB. Find the coordinates of the point C.

Answer:   
Let the coordinates of C be (x, y).
Let AB = m, then AC = 4m.
BC = AC - AB = 4m - m = 3m
\ B divides AC in the ratio 1:3.


x + 12 = 4 15 + y = -28
x = -18 y = -43
\Coordinates of C are (-8, -43).

Question 28

Question:   Find the slope and the angle of inclination q of the lines through each of the following pairs of points.
a) (8,5), (3,5)
b) (9,12), (11,14)

Answer:    a)


b)


c)


d)

Question 29

Question:   Find the value of y, so that the line through A (-3,y) and B (5,9) is parallel to the line through P (9,6) and Q (7,8).

Answer:    Since AB ||PQ, we have
Slope of AB = Slope of PQ

Question 30

Question:   Show that the line through (8, -5) and (4, 7) is perpendicular to the line through (10, 8) and (7, 7).

Answer:   


Since the product of the slopes = -1, the two lines are perpendicular to each other.