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Reference Material for Preparation

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:

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:

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)

Slope of =

iii)

Slope of =

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