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In this lesson, we will learn how to determine if two lines are parallel or perpendicular and use these geometrical relationships to solve problems.

Q1:

Two lines are perpendicular. What will the product of their slopes be?

Q2:

A staight line πΏ has the equation π¦ = 3 π₯ β 2 . Find the equation of the line perpendicular to πΏ that passes through the point ( 4 , 4 ) .

Q3:

The lines π₯ = 3 π‘ β 2 1 , π¦ = 3 π‘ + 2 1 , π§ = 9 π‘ β 2 1 and π₯ = π π‘ β 2 2 , π¦ = π‘ + 1 2 , π§ = π π‘ β 2 2 are parallel. What is π + π ?

Q4:

Which of the following relates the slopes @ π 1 and @ π 2 of two parallel lines?

Q5:

If β ο© ο© ο© ο© β π΄ π΅ β β ο© ο© ο© ο© β πΆ π· and the slope of β ο© ο© ο© ο© β π΄ π΅ = 2 5 , find the slope of β ο© ο© ο© ο© β πΆ π· .

Q6:

Complete the following definition. Two line segments are said to be perpendicular if the product of their slopes is .

Q7:

Two lines π΄ and π΅ have slopes of β 3 5 and 5 3 respectively. Are the two lines parallel or perpendicular?

Q8:

The slope of the straight line that is parallel to the π₯ -axis is .

Q9:

The coordinates of points π΄ , π΅ , πΆ , and π· are ( 3 , 2 ) , ( β 1 , 7 ) , ( 3 , 1 ) , and (9, 2) respectively. Are the line segments π΄ π΅ and πΆ π· perpendicular?

Q10:

Lines π΄ and π΅ are perpendicular to each other and meet at ( β 1 , 4 ) . If the slope of π΄ is 0, what is the equation of line π΅ ?

Q11:

Suppose that πΏ 1 is the line π π₯ β 2 π¦ β 8 = 0 and πΏ 2 the line β 3 π₯ + π¦ + 2 = 0 . Find the value of π so that πΏ β πΏ 1 2 .

Q12:

Find the gradient of the straight line which is parallel to the straight line passing through the points π΄ ( β 7 , 8 ) and π΅ ( 1 , 1 ) .

Q13:

If β ο© ο© ο© ο© β π΄ π΅ β₯ β ο© ο© ο© ο© β πΆ π· and the slope of β ο© ο© ο© ο© β π΄ π΅ = 7 , find the slope of β ο© ο© ο© ο© β πΆ π· .

Q14:

If the two straight lines whose slopes are 3 2 and π 9 are perpendicular, what is the value of π ?

Q15:

Suppose that the points π΄ ( β 5 , 3 ) , π΅ ( β 8 , β 6 ) , πΆ ( 7 , 5 ) , and π· ( π₯ , 8 ) are such that β ο© ο© ο© ο© β π΄ π΅ β₯ β ο© ο© ο© ο© β πΆ π· . What is the value of π₯ ?

Q16:

Which of the following relates the slopes π 1 and π 2 of two perpendicular lines?

Q17:

Let πΏ be the line on points ( β 1 0 , β 1 ) and ( 6 , 5 ) . What is the slope of the perpendicular to πΏ that passes through the origin ( 0 , 0 ) ?

Q18:

Given that π΄ π΅ πΆ π· is a trapezium, where π΄ π΅ β₯ πΆ π· , and the coordinates of points π΄ , π΅ , πΆ , and π· are ( β 5 , β 5 ) , ( β 1 , β 1 ) , ( π₯ , β π₯ ) , and ( β 7 , β 9 ) , respectively, find the coordinates of point πΆ .

Q19:

If the two straight lines 5 π₯ + π π¦ + 1 = 0 and β π = ( 7 , β 7 ) + πΎ ( 6 , 1 ) are parallel, find the value of π .

Q20:

Two lines π΄ and π΅ have slopes of 7 5 and β 5 7 respectively. Are the two lines perpendicular?

Q21:

Let πΏ be the line parallel to the line π¦ + 1 π₯ = β 7 2 and that has π¦ -intercept 7 . Give the equation of πΏ in the form π¦ = π π₯ + π .

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