Math Problem. Parallelism and Perpendicularity?

Question

ok heres the problem.

One line passes through the points (0,-4) and (-1,-7). Another line passes through the points (3,0) and (-3,2). Are these lines parallel, perpendicular or neither?

Please help.

Answer 1

draw the lines! draw the y-axis and x-axis then, join the points. then find the slope! (= rise/run or y/x) if the slope = 0, they are parallel; and for perpendicularity the equation is: slope1 = -(1/slope2). Otherwise, neither!

You can use this strategy to solve this for any points. If you go on and solve this, you will see that they are perpendicular!



P.S. I am asking you to draw them because sometimes drawing figures helps a lot! you can also find the slopes directly from the points! slope1 = (y2 - y1)/(x2-x1) and slope2 = (y4-y3)/(x4-x3)

Slope1 means you use the points for the first line and slope2 means you use the points for the second line

Answer 2

First you must find the slopes of the lines.

Slope is rise over run

This means slope is the change in the y coordinates divided by the change in the x coordinates.

A formula for the slope of a line, given two points of the line, (which define the line) is:



(y2 - y1)/(x2 - x1)



y2 is the y coordinate of the second ordered pair.

y1 is the y coordinate of the first ordered pair.

x2 is the x coordinate of the second ordered pair.

x1 is the x coordinate of the first ordered pair.



for the first line, (y2 - y1)/(x2 - x1) = [-7 - (-4)]/[-1 - 0]

= (-7 + 4)/-1

= -3/-1

= +3



for the second line, (y2 - y1)/(x2 - x1) = (2 - 0)/(-3 - 3)

=2/-6

=-1/3



So the slopes of the lines are +3 and -1/3



so what now?



Parallel lines always have the same slope.

These lines do not have the same slope, so they are not parallel.



Perpendicular lines have slopes that are negative reciprocals of each other.

a reciprocal is a fraction that is "flipped".

so the reciprocal of a/b is b/a.

The negative reciprocal is just the fraction "flipped" and made negative

so the negative reciprocal of -c/d is +d/c

and the negative reciprocal of e/f is -f/e

does this make sense?



In this case, the slopes of the lines ARE negative reciprocals of each other,

so the lines are perpendicular.



this is because +3 = 3/1, which is the negative reciprocal of -1/3.

Answer 3

Parallelism And Perpendicularity

Answer 4

(0,-4), (-1,-7)

m (slope)= -7-(-4)/-1-0 = -3/-1=3



(3,0), (-3,2)

m=2-0/-3-3= 2/-6 = -1/3



The lines are perpendicular because the slope of -1/3 is the negative reciprocal of 3.