# Worksheet: Equations of Parallel and Perpendicular Lines

In this worksheet, we will practice writing the equation of a line parallel or perpendicular to another line.

Q1:

Write, in the form , the equation of the line through that is parallel to the line .

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Q2:

Find, in slope-intercept form, the equation of the line parallel to that passes through point .

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Q3:

A straight line has the equation . Find the equation of the line parallel to that passes through the point .

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Q4:

Write, in the form , the equation of the line through that is parallel to the line .

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Q5:

Write, in the form , the equation of the line through that is parallel to the line .

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Q6:

Find, in slope-intercept form, the equation of the line parallel to that passes through point .

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Q7:

Find, in slope-intercept form, the equation of the line parallel to that passes through point .

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Q8:

Find, in slope-intercept form, the equation of the line perpendicular to that passes through the point .

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Q9:

Suppose that the points , , and form a right triangle at . What is the value of ?

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Q10:

Given that the coordinates of the points , , , and are , , , and , respectively, determine whether and are parallel, perpendicular, or neither.

• Aperpendicular
• Bneither
• Cparallel

Q11:

Determine, in slope-intercept form, the equation of the line passing through perpendicular to the line passing through and .

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Q12:

Write, in the form , the equation of the line that is parallel to the line and that intercepts the -axis at 1.

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Q13:

If and , find the cartesian equation of the straight line passing through the point of division of internally in the ratio and perpendicular to the straight line whose equation is .

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Q14:

Consider the triangle on , , and , and let be the midpoint of . Now let on be the intersection of the parallel to through the point . Find the equation of in the form .

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Q15:

Lines and are perpendicular to each other and meet at . If the slope of is 0, what is the equation of line ?

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Q16:

Determine whether the lines and are parallel, perpendicular, or neither.

• Aperpendicular
• Bparallel
• Cneither

Q17:

If a line is perpendicular to the line , and passes through the points and , what is the value of ?

Q18:

Suppose that is the line , and the line . Find the value of so that .

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Q19:

If the two straight lines and are perpendicular, find the value of .

Q20:

Which of the following lines is perpendicular to the line ?

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Q21:

Given and , find the equation of the perpendicular to that passes through the midpoint of this line segment. Give your answer in the form .

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Q22:

Write, in the form , the equation of the line through that is perpendicular to , where .

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Q23:

Find the equation of the straight line passing through the point and perpendicular to the straight line passing through the points and .

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Q24:

Lines and are perpendicular to each other and meet at . If the slope of is , what is the equation of line ?

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Q25:

The straight lines and are parallel. What is the value of ?