Introduction to learn online perpendicular lines:
Perpendicular means nothing but when two lines are cross in either direction and form right or 90 degree angles, so a horizontal line and a vertical line that cross are perpendicular because they form right angles.
Perpendicular lines are two lines which meet at a right angle. Right angle is 90degrees. Please express your views of this topic Slope of a Perpendicular Line by commenting on blog.
Learn perpendicular lines online through examples
1)Find the equation of the perpendicular line to y = `(1)/(2)` x-5, passing through the point (4, 10).
Learn perpendicular lines online by using slope-intercept form:
Since the original line has a slope of `(1)/(2)` , a perpendicular line must have a slope of -2.
Therefore, the equation must look like y = -2x + b.
Substituting the given point in place of x and y we have: 10 = -2(4) + b. Solving, we find that b = 18.
The equation is y = -2x + 18.
Learn perpendicualr lines online by using point-slope form:
Again, the perpendicular slope is m = -2. The equation must look like y - y1= -2(x - x1).
Substituting the given point in place of x1 and y1 we have y - 10 = -2(x - 4).
Rearranging yields y - 10 = -2x + 8 or y = -2x + 18.
2) Show that the lines 6x +3y +9 = 0 and 3x-5y+7 = 0 are perpendicular.
Solution: Given equation of lines as 6x + 3y + 9 = 0 and 3x + 5y+7 = 0
First line: 6x + 3y + 9 = 0 Second line: 3x - 5y + 7 = 0
6x + 3y + 9 - 9 = 0 -9 3x - 5y + 7 -7 = 0 -7
6x + 3y = -9 3x - 5y = -7
6x -6x + 3y = -9 - 5x 3x - 3x - 5y = -7 -3x
3y = -6x - 9 -5y = -3x-7
3y/3 = (-6x-9)/3 5y/5 = (3x+7)/5
y = -5/3x -3 y = 3/5x +7/5
compare with y = mx + b compare with y = mx +b
m =`(-5)/(3)` and b = -3 m = `(3)/(5)` and b = `(7)/(5)`
Condition for lines to be perpendicular is m 1 * m2 = -1
Here, m 1 = `(-5)/(3)` and m 2 = `(3)/(5)` ,
m1 * m 2 = `(-5)/(3)` *`(3)/(5)` = -1
Therefore the 5x +3y +9 = 0 and 3x-5y+7 = 0 are perpendicular lines.
I have recently faced lot of problem while learning need help with math problems for free, But thank to online resources of math which helped me to learn myself easily on net.
learn perpendicular online -formula
Two lines are perpendicular to each other when the product of their slopes is -1
Let slope of first line is m1
Slope of second line is m2
m1 * m2 = -1
Slope of a line between points (x1,y1) and (x2,y2) is m =`(y_(2)- y_(1))/(x_(2)- x_(1))`
Equation of line in slope intercept form is y = mx +b , where m is the slope of line and b is the y intercept of line
The equation of all lines perpendicular to the line ax +by +c = 0 can be written as bx –ay +k = 0 for different values of k
Perpendicular means nothing but when two lines are cross in either direction and form right or 90 degree angles, so a horizontal line and a vertical line that cross are perpendicular because they form right angles.
Perpendicular lines are two lines which meet at a right angle. Right angle is 90degrees. Please express your views of this topic Slope of a Perpendicular Line by commenting on blog.
Learn perpendicular lines online through examples
1)Find the equation of the perpendicular line to y = `(1)/(2)` x-5, passing through the point (4, 10).
Learn perpendicular lines online by using slope-intercept form:
Since the original line has a slope of `(1)/(2)` , a perpendicular line must have a slope of -2.
Therefore, the equation must look like y = -2x + b.
Substituting the given point in place of x and y we have: 10 = -2(4) + b. Solving, we find that b = 18.
The equation is y = -2x + 18.
Learn perpendicualr lines online by using point-slope form:
Again, the perpendicular slope is m = -2. The equation must look like y - y1= -2(x - x1).
Substituting the given point in place of x1 and y1 we have y - 10 = -2(x - 4).
Rearranging yields y - 10 = -2x + 8 or y = -2x + 18.
2) Show that the lines 6x +3y +9 = 0 and 3x-5y+7 = 0 are perpendicular.
Solution: Given equation of lines as 6x + 3y + 9 = 0 and 3x + 5y+7 = 0
First line: 6x + 3y + 9 = 0 Second line: 3x - 5y + 7 = 0
6x + 3y + 9 - 9 = 0 -9 3x - 5y + 7 -7 = 0 -7
6x + 3y = -9 3x - 5y = -7
6x -6x + 3y = -9 - 5x 3x - 3x - 5y = -7 -3x
3y = -6x - 9 -5y = -3x-7
3y/3 = (-6x-9)/3 5y/5 = (3x+7)/5
y = -5/3x -3 y = 3/5x +7/5
compare with y = mx + b compare with y = mx +b
m =`(-5)/(3)` and b = -3 m = `(3)/(5)` and b = `(7)/(5)`
Condition for lines to be perpendicular is m 1 * m2 = -1
Here, m 1 = `(-5)/(3)` and m 2 = `(3)/(5)` ,
m1 * m 2 = `(-5)/(3)` *`(3)/(5)` = -1
Therefore the 5x +3y +9 = 0 and 3x-5y+7 = 0 are perpendicular lines.
I have recently faced lot of problem while learning need help with math problems for free, But thank to online resources of math which helped me to learn myself easily on net.
learn perpendicular online -formula
Two lines are perpendicular to each other when the product of their slopes is -1
Let slope of first line is m1
Slope of second line is m2
m1 * m2 = -1
Slope of a line between points (x1,y1) and (x2,y2) is m =`(y_(2)- y_(1))/(x_(2)- x_(1))`
Equation of line in slope intercept form is y = mx +b , where m is the slope of line and b is the y intercept of line
The equation of all lines perpendicular to the line ax +by +c = 0 can be written as bx –ay +k = 0 for different values of k
No comments:
Post a Comment