10.2 PERPENDICULAR LINES

The equation of a line is in the form:

m is the

b is the

y =mx+b

slope

y-intercept

Slopes of perpendicular lines are .

To write the equation of a perpendicular line, first find the perpendicular slope, then use a point on the perpendicular line and point-slope form to find the equation of the line.

Review, point slope form is:

oppositereciprocals

y−y1 =m x−x1( )

Determine the equation of the line passing through the given point and perpendicular to the line with the given equation.

1. 5y + 3x=6; 3,−2( )

Determine the equation of the line passing through the given point and perpendicular to the line with the given equation.

2. 4y =7x+1; −1,−2.5( )

The slope of the line containing the points and is :

x1, y1( )x2 , y2( )

m =y2 −y1

x2 −x1

Determine an equation of the line containing U and perpendicular to the line passing through A and S.

3. A 6,−1( ), S −2,5( ),U −4,−3( )

Determine an equation of the line containing U and perpendicular to the line passing through A and S.

4. A2

5,1

4⎛⎝⎜

⎞⎠⎟, S −

15,74

⎛⎝⎜

⎞⎠⎟,U

32,4⎛

⎝⎜⎞⎠⎟

Recall from geometry, the perpendicular bisector of a segment is the line passing through the

of the segment and to the line

containing the segment.

midpointperpendicular

Determine the equation for the perpendicular bisector for the line segment with the given endpoints.

5. 6,−8( ), 10,−14( )

Determine the equation for the perpendicular bisector for the line segment with the given endpoints.

6. 1

3,5

6⎛⎝⎜

⎞⎠⎟, −1,

12

⎛⎝⎜

⎞⎠⎟