# Straight Lines - Online Test

Q1. The point which divides the joint of ( 1, 2 ) and ( 3,4 ) externally in the ratio 1 : 1 .
Explaination / Solution:

The point which divides the line in the ratio m:n externally is given by x =

Substituting the values we get,

x =  which is undefined.

Q2. The distance of the point ( x, y ) from the origin is
Explaination / Solution:

Distance between two points is given by $\sqrt{\left(}$

Therefore  the distance from the origin to the point (x,y) is  =

Q3. Slope of a line is not defined if the line is
Explaination / Solution:

Vertical lines hve undefined slopes. Hence a line which is parallel to Y-axis has undefined slopes.

Q4. The line through the points (a , b) and (- a , - b) passes through the point
Explaination / Solution:

Equation of a line passing through (x1,y1) and (x2,y2

=

Substituting the given values we get,

=

That is  =

On cross multiplying and reaaranging we get,

bx - ay = 0

If this passes through the given point (a2,ab) then

b(a2) - a(ab) = 0

Q5. Projection (the foot of perpendicular) from ( x , y ) on the x – axis is
Explaination / Solution:

Let L be the foot of the perpendicular from the X axis. Therefore its y coocrdinate is zero Therefore the coordiantes of the point L is (x,0)

Q6. The equation represents all lines through the point  except the line
Explaination / Solution:

The vertical lines which are parallel to Y axis has undefined slopes. Hence the slope of the line 'm' will be undefined.

Therefore the above equation of the line will represent all lines through () except the line parallel to Y- axis

Q7. Slope of any line parallel to X axis is
Explaination / Solution:

Since the angle made with x axis is zero, since tanθ is the slope. Then tan0 = 0 Hence the slpoe of the line parallel to X-axis is zero

Q8. The distance between the parallel lines 3x + 4y + 13 = 0 and 3x + 4y – 13 = 0 is
Explaination / Solution:

Distance between parallel lines is given by

Now substituting the values we get,

=

Q9. The straight lines x + y = 0 , 3x - y – 4 = 0 , x + 3y – 4 = 0 form a triangle which is
Explaination / Solution:

The lines formed by these lines is right angled, triangle.

Two lines are perpendicular to each other if the product  od their slopes is -1

Slope of the lines  3x - y – 4 = 0 , x + 3y – 4 = 0 are 3 and -1/3 respectively.

The product of these slopes is -1

Hence the lines3x - y – 4 = 0 , x + 3y – 4 = 0  are perpendicular to each other.

Therefore the triangle formed by these lines is a right angled triangle.

Q10. The lines 2x – 3y = 5 and 6x – 9y – 7 = 0 are
Explaination / Solution:

The given lines are paraallel lines

Condition for the line to be parallel is  $\ne$

substituting the values,

=$\ne$

Hence they are parallel lines.