Question 1: Find the slope of the lie whose inclination is:
Answer:
Question 2: Find the inclination of the line whose slope is:
Answer:
Question 3: Find the slope of the line passing through the following pairs of points:
Answer:
Question 4: Find the slope of the line parallel to AB if:
Answer:
Question 5: Find the slope of the line perpendicular to AB if:
Answer:
Question 6: The line passing through is parallel to the line passing through
. find
Answer:
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:
Since the two lines are perpendicular 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:
is perpendicular to
.
is a right angled triangle.
Question 9: Without using distance formula, show that the points are the vertices of a parallelogram.
Answer:
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:
be the vertices of the quadrilateral.
is a parallelogram.
Question 11: Show that the points are collinear.
Answer:
are collinear.
Question 12: Find , if the slope of the line joining
is
Answer:
Given slope of the line joining is
.
Question 13: The side of an equilateral triangle
is parallel to the
. Find the slopes of all the sides.
Answer:
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:
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:
Let slope of Altitude
be the midpoint of
Therefore coordinates 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:
Question 17: Find the slope and the inclination of the line if:
Answer:
Inclination :
Inclination :
Inclination :
Question 18: The points are collinear. Find
Answer:
are collinear
Question 19: The points are collinear. Find
Answer:
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:
Inclination :
Inclination :
Question 21: Find the value(s) of so that
will be parallel to
Given:
Answer:
=
=