3.9- Parallel and perpendicular lines in the coordinate plane

Write the midpoint as a

Coordinate

A( -1, 1), B(4, -1), C(3, 4) and D(-1, 6) are the vertices of quadrilateral ABCD. Are the diagonals of ABCD perpendicular? (Draw a sketch and follow through with work to help you find out.)

Find the slope of each diagonal (ac) and (bd) Then see if the slopes are opposite reciprocals They were not so the Diagonals are not perpendicular because the slopes are not opposite reciprocals.

Write the quation of a line passing through the point x,y and perpendicular to the line 2x+y=2

First change 2x+y into slope-int y=-2x+2 Then since perpendicular is opposite reciprocal you find that from the slope in the equation given Then you plug in the points given to find b Write as one big equation

Find the equation of the perpendicular bisector of the segment with endpoint 2,9 and -6,-7

First you find the regular slope Draw an image Then you find the opposite reciprocal because you want perpendicular Then you find the points you are going to plug in by you find the coordinates of the midpoint by averaging the two coordinates given Then you plug in the midpoint coordinates to solve for b Then you write it as one big equation Need point on perpendicular line to plug in and you know that midpoint is a point on perpendicular bisector

Parallel slope theorem

In a coordinate plane, two distinct lines are parallel if and only if their slopes are the same.

Perpendicular slope theorem

In a coordinate plane, two lines are perpendicular if and only if their slopes are opposite reciprocals. Opposite means like if it was negative then its positive and vise versa

Slope is

M=y2-y1/ x2 - x1 Label the coordinates with x and y to help you

Don't forget

Negative for reciprocal

Remember when finding the perpendicular bisector of a line with two coordinates

Once you find a slope of that line, you have to find the opposite reciprocal for perpendicular bisector Then you find the midpoint and plug it in to find b

Remmeber to do

Opposite reciprocal for perpendicular

Find b by

Plugging in a point for x and y

Perpendicular means opposite

Reciprocals

Parallel means

Same slope, but different y-int or they would be the same line Perpendicular are the opposite reciprocal, can have the same y-int

Always

Simplify your answer

When it says write an equation it wants it in

Slope-intercept form All answers in slope-intercept

Trick is to

Take your time and don't make dumb mistakes Be careful

You would say like yes the lines are parallel because

The slopes are the same

O/1 is (0)

Undefined slope

Line 1 contains (−2, 1) and (4, 3) and line 2 contains (5, 3) and (3, g). What value of g makes 1 and 2 perpendicular?

Use blanks Perpendicular means opposite reciprocal Can cross-multiple to check

If it gives you two coordinates and tells you to find the slope of a parallel line

You first find the slope of the two coordinates Then you know because of the parallel slope theorem that the slope is the same

Write the equation of a line passing through x,y and parallel to line y=2x+b

You know that parallel means same slope so the slope will be 2 Y=2x +b Then you solve for b by plugging in x and y of the coordinate you were given Once you find out what b is you write it as one equation with 2 as the slope and b as a #

If you were given the endpoint as a coordinate and the midpoint how do you find the coordinate of the other endpoint

You leave blanks for the midpoint formula 5 the x of the midpoint= -3+-/2, it must equal 13 Given one out of the two coordinates that were averaged to find the midpoint

Slope formula is

m=y2-y1/x2-x1

Even if they draw them looking like they are parallel or perpendicular, doesn't mean

they are parallel or perpendicular Have to find slope to determine that

Be careful with your math

!

Opposite reciprocal of 1 is

-1