Solved Line Word Problems

Solutions

1Find the symmetric point A', of the point A = (3, 2), with the line of symmetry: r ≡ 2x + y − 12 = 0.

2Identify the type of triangle formed by the points: A = (4, −3), B = (3, 0) and C = (0, 1).

3Calculate the equation of the line that passes through the point P = (−3, 2) and is perpendicular to the line r ≡ 8x − y − 1 = 0.

4The line r ≡ x + 2y − 9 = 0 is the perpendicular bisector of the line segment AB whose endpoint A has the coordinates (2, 1). Find the coordinates of the other endpoint.

5Calculate the angle between the lines whose equations are:

1 Line Word Problem

2 Line Word Problem

6A straight line is parallel to the line r ≡ 5x + 8y − 12 = 0, and it is 6 units from the origin. What is the equation of this line?

7Determine the equations of the angle bisectors formed by the lines:

Line Word Problem

8The vertices of a parallelogram are A = (3, 0), B = (1, 4), C = (−3, 2) and D = (−1, −2). Calculate the area.

9Given the triangle formed by the points A = (−1, −1), B = (7, 5) and C = (2, 7), calculate the equations of the heights and determine the orthocenter of the triangle.

10A line is perpendicular to the line r ≡ 5x − 7y + 12 = 0 and it is 4 units away from the origin. Determine the equation of this line.

1

Find the symmetric point A', of the point A = (3, 2), with the line of symmetry: r ≡ 2x + y − 12 = 0.

Symmetric Point

Line Exercise

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2

Identify the type of triangle formed by the points: A = (4, −3), B = (3, 0) and C = (0, 1).

Triangle


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3

Calculate the equation of the line that passes through the point P = (−3, 2) and is perpendicular to the line r ≡ 8x − y − 1 = 0.

Line Exercise

Line Solution

 

4

The line r ≡ x + 2y − 9 = 0 is the perpendicular bisector of the line segment AB whose endpoint A has the coordinates (2, 1). Find the coordinates of the other endpoint.

Perpendicular Bisector

Perpendicular Lines

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5

Calculate the angle between the lines whose equations are:

1    Line Exercise

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2    Line Exercise

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6

A straight line is parallel to the line r ≡ 5x + 8y − 12 = 0, and it is 6 units from the origin. What is the equation of this line?

Line Operations

Line Calculations

Line Solution

 

7

Determine the equations of the angle bisectors formed by the lines:

Line Exercise

Line Calculations

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Line Solution


8

The vertices of a parallelogram are A = (3, 0), B = (1, 4), C = (−3, 2) and D = (−1, −2). Calculate the area.

Vertices of a Parallelogram

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9

Given the triangle formed by the points A = (−1, −1), B = (7, 5) and C = (2, 7), calculate the equations of the heights and determine the orthocenter of the triangle.

Heights of a Triangle

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10

A line is perpendicular to the line r ≡ 5x − 7y + 12 = 0 and it is 4 units away from the origin. Determine the equation of this line.

Line Calculations

Line Calculations

Line Solution