Line Problems

Solutions

1Write the equation (in all possible forms) of the line that passes through the points A = (1, 2) and B = (2, 5).

2Identify the type of triangle formed by the points: A = (6, 0), B = (3, 0) and C = (6, 3).

3Determine the slope and y-intercept of the line 3x + 2y − 7 = 0.

4 Find the equation of the line r which passes through the point A = (1, 5) and is parallel to the line s ≡ 2x + y + 2 = 0.

5 Find the equation of the line that passes through the point (2, −3) and is parallel to the straight line that joins the points (4, 1) and (−2, 2).

6 The points A = (−1, 3) and B = (3, −3) are vertices of an isosceles triangle ABC that has its apex C on the line 2x − 4y + 3 = 0. If AC and BC are the equal sides, calculate the coordinates of Point C.

7 The line r ≡ 3x + ny − 7 = 0 passes through the point A = (3, 2) and is parallel to the line s ≡ mx + 2y −13 = 0. Calculate the values of m and n.

8Given triangle ABC with coordinates A = (0, 0), B = (4, 0) and C = (4, 4), calculate the equation of the median that passes through the vertex C.

9A parallelogram has a vertex A = (8, 0), and the point of intersection of its two diagonals is M = (6, 2). If the other vertex is at the origin, calculate:

1 The other two vertices.

2 The equations of the diagonals.

3 The length of the diagonal.

 

1

Write the equation (in all possible forms) of the line that passes through the points A = (1, 2) and B = (2, 5).

Two-Point Form Equation.

formulas

General form.

General Form Equation

Slope–intercept form.

Slope-Intercept Form

Point–slope form.

Point-Slope Form

Parametric form.

Components of a Line

Parametric Form


2

Identify the type of triangle formed by the points: A = (6, 0), B = (3, 0) and C = (6, 3).

Triangle

Triangle Calculations

Triangle Calculations

Triangle Calculations

Isosceles Triangle

Right Triangle


3

Determine the slope and y-intercept of the line 3x + 2y − 7 = 0.

Line Example

Slope and Y-Intercept

4

Find the equation of the line r which passes through the point A = (1, 5) and is parallel to the line s ≡ 2x + y + 2 = 0.

Parallel Lines

Slope Calculations

Line Operations

Line Solution

 

5

Find the equation of the line that passes through the point (2, −3) and is parallel to the straight line that joins the points (4, 1) and (−2, 2).

Line Calculations

Line Calculations

Line Operations

 

6

The points A = (−1, 3) and B = (3, −3) are vertices of an isosceles triangle ABC that has its apex C on the line 2x − 4y + 3 = 0. If AC and BC are the equal sides, calculate the coordinates of Point C.

Isosceles Triangle


Line Operations

Line Operations

Line Operations

Line Calculations

Line Calculations

Line Solution

 

7

The line r ≡ 3x + ny − 7 = 0 passes through the point A = (3,2) and is parallel to the line s ≡ mx + 2y −13 = 0. Calculate the values of m and n.

Line Operations

Line Calculations

Parallel Lines

Line Solution

 

8

Given triangle ABC with coordinates A = (0, 0), B = (4, 0) and C = (4, 4), calculate the equation of the median that passes through the vertex C.

Median of a Triangle

Line Operations

Equation of the Line

 

9

A parallelogram has a vertex A = (8, 0), and the point of intersection of its two diagonals is M = (6, 2). If the other vertex is at the origin, calculate:


1 The other two vertices.

Line Operations

formulas

Line Operations

formulas


2 The equations of the diagonals.

Line Operations

Line Calculations

Line Operations

Line Calculations


3 The length of the diagonal.

Line Calculations

Line Calculations