Question 1: Find the slope of the lie whose inclination is:
i) ii)
iii)
iv)
Answer:
i)
Slope
ii)
Slope
iii)
Slope
iv)
Slope
Question 2: Find the inclination of the line whose slope is:
i) ii)
iii)
iv)
Answer:
i)
Slope
ii)
Slope
iii)
Slope
iv)
Slope
Question 3: Find the slope of the line passing through the following pairs of points:
i)
ii)
iii)
Answer:
i)
Let
Therefore Slope
ii)
Let
Therefore Slope
iii)
Let
Therefore Slope
Question 4: Find the slope of the line parallel to AB if:
i)
ii)
Answer:
i)
Slope
Therefore the slope of the line parallel to
ii)
Slope
Therefore the slope of the line parallel to
Question 5: Find the slope of the line perpendicular to AB if:
i)
ii)
Answer:
i)
Slope
Therefore the slope of the line perpendicular to
ii)
Slope
Therefore the slope of the line parallel to
Question 6: The line passing through is parallel to the line passing through
. find
.
Answer:
The slope of line passing through
The slope of line passing through
Since the two lines are parallel to each other, their slope must be equal. Therefore
Question 7: The line passing through is perpendicular to the line passing through
. Find
.
Answer:
The slope of line passing through
The slope of line passing through
Since the two lines are perpendiculare to each other, the product of their slopes should be equal to . Therefore
Question 8: Without using distance formula, show that the points are the vertices of a right-angled triangle.
Answer:
Slope of
Slope of
Slope of
Since
is perpendicular to
.
Therefore is a right angled triangle.
Question 9: Without using distance formula, show that the points are the vertices of a parallelogram.
Answer:
Slope of
Slope of
Slope of
Slope of
Therefore and
Therefore is a parallelogram.
Question 10: are the vertices of a quadrilateral. Show that the quadrilateral, obtained on joining the mid-points of its sides is a parallelogram.
Answer:
Let be the vertices of the quadrilateral.
Mid-point of
Mid-point of
Mid-point of
Mid-point of
Slope of
Slope of
Slope of
Slope of
Since and
is a parallelogram.
Question 11: Show that the points are collinear.
Answer:
Slope of
Slope of
Since are collinear.
Question 12: Find , if the slope of the line joining
is
.
Answer:
Given slope of the line joining is
.
Slope of
Question 13: The side of an equilateral triangle
is parallel to the
. Find the slopes of all the sides.
Answer:
Slope of
Slope of
Slope of
Question 14: The side of a square
is parallel to the
. Find the slopes of all its sides. Also, find: i) The slope of the diagonal
, ii) The slope of the diagonal
.
Answer:
Slope of
Slope of
Slope of
Slope of
Slope of
Slope of
Question 15: are the vertices of a triangle
. Find: i) The slope of the altitude of
ii) The slope of the median
and iii) The slope of the line parallel to
.
Answer:
Slope of
Let slope of Altitude
Therefore
Let be the midpoint of
Therefore coordinates of
Slope of
Slope of
Therefore slope of line parallel to
Question 16: The slope of the side
of a rectangle
is . Find: i) The slope of the side
, ii) The slope of the side
.
Answer:
Since
Since
Question 17: Find the slope and the inclination of the line if:
i)
ii)
iii)
Answer:
i)
Let
Therefore Slope
Inclination :
ii)
Let
Therefore Slope
Inclination :
iii)
Let
Therefore Slope
Inclination :
Question 18: The points are collinear. Find
.
Answer:
and
are collinear
Question 19: The points are collinear. Find
.
Answer:
and
are collinear
Question 20: Plot he points on a graph paper. Connect
, and also
. Which segment appears to have the steeper slope,
? Justify your conclusion by calculating the slopes of
.
Answer:
Let and
Therefore Slope of
Inclination :
Let
Therefore Slope of
Inclination :
Question 21: Find the value(s) of so that
latex RS. Given:
i)
ii)
iii)
Answer:
i) and
Slope of =
ii) and
Slope of =
iii) and
Slope of Slope