# 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.

**Q9: **

Suppose that the points , , and form a right-angled 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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**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 ?