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In this lesson, we will learn how to determine whether graphs of lines are parallel or perpendicular.

Q1:

Two lines and have gradients of and respectively. Are the two lines parallel?

Q2:

Two lines have slopes of 6 5 and 1 2 1 0 . Are the two lines parallel?

Q3:

Describe the relative positions of the straight lines 2 π₯ = 3 and 5 π¦ = 8 .

Q4:

Describe the relative positions of the straight lines 4 π₯ β 4 π¦ = 5 and 3 2 π₯ β 3 2 π¦ = 4 0 .

Q5:

How would you describe the relation between the lines π¦ = 1 7 π₯ + 9 and β π₯ + 7 π¦ + 4 = 0 ?

Q6:

How would you describe the relation between the lines π¦ = π₯ β 9 and β π₯ + π¦ β 4 = 0 ?

Q7:

How would you describe the relation between the lines π¦ = β 7 2 π₯ β 2 and 7 π₯ + 2 π¦ + 4 = 0 ?

Q8:

How would you describe the relation between the lines π¦ = β 4 π₯ β 1 2 and 8 π₯ + 2 π¦ + 1 = 0 ?

Q9:

What is the value of π , if lines β 2 π₯ + π π¦ + 6 = 0 and β π₯ β 4 π¦ β 3 = 0 are parallel?

Q10:

What is the value of π , if lines 5 π₯ + π π¦ β 2 = 0 and β 4 π₯ β 5 π¦ + 1 = 0 are parallel?

Q11:

The line πΏ 1 passes through the points ( 3 , 3 ) and ( β 1 , 0 ) , and the line πΏ 2 passes through the points ( β 3 , 2 ) and ( 0 , β 2 ) . Are the two lines perpendicular?

Q12:

Let πΏ be the line through the points ( β 7 , β 7 ) and ( β 9 , 6 ) and π the line through ( 1 , 1 ) and ( 1 4 , 3 ) . Which of the following is true about the lines πΏ and π ?

Q13:

Let πΏ be the line through the points ( β 4 , 9 ) and ( 0 , β 5 ) and π the line through ( β 1 2 , 1 7 ) and ( β 2 6 , 1 3 ) . Which of the following is true about the lines πΏ and π ?

Q14:

Let πΏ be the line through the points ( β 7 , 6 ) and ( β 2 , 1 ) and π the line through ( β 1 2 , 4 ) and ( β 7 , β 1 ) . Which of the following is true about the lines πΏ and π ?

Q15:

If the line that passes through the points π΄ ( 6 , 0 ) and π΅ ( 4 , β 6 ) is perpendicular to the line passing through the points πΆ ( β 9 , 1 9 ) and π· ( π₯ , 1 5 ) , what is the value of π₯ ?

Q16:

The line on the points ( 1 0 , π + 2 ) and π΅ ( 7 , 1 0 ) is parallel to one that makes an angle of 1 0 0 β with the positive π₯ -axis. Determine π to the nearest integer.

Q17:

Two lines and have gradients of and respectively. Are the two lines perpendicular?

Q18:

The line through points ( 5 , 7 ) and ( 1 , π ) is parallel to the line π β 3 π₯ β 7 = 0 . Find π .

Q19:

The line through points ( β 7 , 0 ) and ( β 2 , π ) is perpendicular to the line β 8 π β 4 π₯ + 9 = 0 . Find π .

Q20:

The line through points ( β 1 , β 9 ) and ( β 4 , π ) is perpendicular to the line 8 π β π₯ β 6 = 0 . Find π .

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