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In this lesson, we will learn how to create the equations of parallel and perpendicular lines.

Q1:

Suppose that the points π΄ ( β 3 , β 1 ) , π΅ ( 1 , 2 ) , and πΆ ( 7 , π¦ ) form a right-angled triangle at π΅ . What is the value of π¦ ?

Q2:

Given that the coordinates of the points π΄ , π΅ , πΆ , and π· are ( β 1 5 , 8 ) , ( β 6 , 1 0 ) , ( β 8 , β 7 ) , and ( β 6 , β 1 6 ) , respectively, determine whether β ο© ο© ο© ο© β π΄ π΅ and β ο© ο© ο© ο© β πΆ π· are parallel, perpendicular, or neither.

Q3:

Determine, in slope-intercept form, the equation of the line passing through π΄ ( 1 3 , β 7 ) perpendicular to the line passing through π΅ ( 8 , β 9 ) and πΆ ( β 8 , 1 0 ) .

Q4:

Write, in the form π¦ = π π₯ + π , the equation of the line that is parallel to the line β 4 π₯ + 7 π¦ β 4 = 0 and that intercepts the π¦ -axis at 1.

Q5:

If π΄ ( 3 , β 1 ) and π΅ ( β 4 , β 8 ) , find the cartesian equation of the straight line passing through the point of division of π΄ π΅ internally in the ratio 4 βΆ 3 and perpendicular to the straight line whose equation is 1 0 π₯ + 3 π¦ β 6 5 = 0 .

Q6:

If the slope of the straight line ( 3 π + 7 ) π₯ + 4 π π¦ + 4 = 0 equals β 1 , find the value of π .

Q7:

Find the slope of the line β 2 π₯ + 3 π¦ β 2 = 0 and the π¦ -intercept of this line.

Q8:

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΅ ?

Q9:

Determine whether the lines π¦ = β 1 7 π₯ β 5 and π¦ = β 1 7 π₯ β 1 are parallel, perpendicular, or neither.

Q10:

Given that the points π΄ ( 1 2 , 1 0 ) and π΅ ( π₯ , β 8 ) lie on a line that has a slope of 1, determine the value of π₯ .

Q11:

If a line πΏ is perpendicular to the line β 2 π¦ + 1 0 = β 6 π₯ + 7 , and πΏ passes through the points π΄ ( π , β 1 0 ) and π΅ ( β 7 , 2 ) , what is the value of π ?

Q12:

Suppose that πΏ 1 is the line π π₯ β π¦ + 1 5 = 0 , and πΏ 2 the line β 2 π₯ 3 + π¦ 2 = β 2 3 . Find the value of π so that πΏ β«½ πΏ 1 2 .

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