have a triangle ABC

Question

A(-2, 0), B(, 3) and C(5, -1).  Need to write the equation of a line through C that is parallel to line AB. 

Write an equation of a line through B that is perpendicular to line AC.  I have y= 1x -3 for 1st equation.  y=7x-11 for second.  Correct? or did I goof?

Answer 1

For the first part

 

 

Parallel lines have the same slope.  We need to find the slope of line AB using the points given.

 

A(-2, 0)    and     B(2, 3)

 

Slope = (3 - 0) / (2 - (-2))

         = 3 / 4

 

So far, the equation of the line is

 

y = (3/4)x + b

 

 

Next, plug in the values of point C into this equation to solve for b. 

 

-1 = (3/4)(5) + b

-1 = 15/4 + b

-19/4 = b

 

The equation of the line is

 

y = (3/4)x - (19/4)

 

 

For the second part

 

Perpendicular lines have negative reciprocal slopes.  We need to find the slope of AC using the given points.

 

A(-2, 0)      and      C(5, -1)

 

Slope = (-1 - 0) / (5 - (-2))

         = -1 / 7

 

So far the equation of the line is

 

y = 7x + b

 

 

Next, plug in the values of point B into the equation to find b.

 

3 = 7(2) + b

3 = 14 + b

- 11 = b

 

The equation of the line is

 

y = 7x - 11

 

 

This confirms that you were correct for the second part.