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Question 1: Find the Slope of the lie whose inclination is:
i) ii) iii) iv)
Answer:
i)
ii)
iii)
iv)
Question 2: Find the inclination of the line whose slope is:
i) ii) iii) iv)
Answer:
i)
ii)
iii)
iv)
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
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
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:
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:
Let
Therefore Slope of
Inclination :
Let
Therefore Slope of
Inclination :
Question 21: Find the value(s) of latex PQ will be parallel to latex P (2, 4), Q (3, 6), R (8, 1) \ and \ S (10, k) &s=0$
ii)
iii)
Answer:
i)
Slope of =
ii)
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