Solve Perpendicular Problems

Introduction

In a plane, if any two non-linear lines are perpendicular, then their product of slope of two lines is -1. Any horizontal line is perpendicular to vertical line.

This can be represented as m1 * m2 = -1

Here, m1 is the slope of line -1 and m2 is slope of line-2

Example for Solve Perpendicular Problems:

Slope and Perpendicular Lines in problems:

1. If two non vertical lines are perpendicular and the product of slope is -1.

2. If the product of the slope of two lines is -1, then the lines are perpendicular.

3. A horizontal line is perpendicular to a vertical line.

Perpendicular bisector

– The bisector of a segment perpendicular to it

Perpendicular lines

– 2 segments, rays, or lines that form a 90 degree angle

Perpendicular planes

– Planes in which any 2 intersecting lines, one in each plane, form a right angle

Solve Perpendicular Problems:

Solve the given equation y – 5x = 10. Find the slope which is perpendicular to the line

Solution:

y – 5x = 10

Rearrange the problem in slope intercept form,

y = 5x + 10 (slope intercept form is y = mx + c)

the slope of the line-1m is 5,

5(m) = -1

Here ‘m’ stands for the slope of the perpendicular line.

m = ‘- 1 /5’

By solving, the slope of line perpendicular to the given line is ‘- 1 / 5’ .

solve the equation of the line that passes through (4, 6) and is perpendicular to the line whose equation is y = ‘3 / (5 x + 3)’

Solution:

The slope is ‘3/5’ ( here y = ‘3 /(5 x + 3)’ is in slope intercept form).

Use (4,6) and the slope’ 3 / 5′ to find the y -intercept.

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y = mx + b

solve this by using substitution property

6 = (‘3 / 5’ )* (4 ) + b

6 =’ 12 / 5′ + b

‘(6 – 12) / 5’ = b

‘(30 – 12 )/ 5’ = b

’18 / 5′ =b

So, the equation of line is y =’ 3 /( 5 x)’ + ’18 / 5′

Write an equation of a line perpendicular to 4y – x = 20 and containing the point (2, -3).

Rewrite the equation in Slope-intercept form.

y = .25x + 5

We know that the slope of a Perpendicular line is -4

25 * -4 = -1.

Now the given points and the slope into a slope-intercept equation to find the y intercept.

-3 = (-4)2 + b

Solve for b.

b = 5

Now, you need to write an equations for a line perpendicular to 4y – x = 20. The answer is the following equation:

y = -4x + 5.