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In a plane, line b is perpendicular to line f, line f is perpendicular to line g, and line h is parallel to line f. Which of the following must be true? hmc047-1.jpgg b || h g || f fmc047-2.jpg

In a plane, line b is perpendicular to line f, line f is perpendicular to line g, and line h is parallel to line f. Which of the following must be true? hmc047-1.jpgg b || h g || f fmc047-2.jpgh

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The equation of the straight line PQ is 3-2kx+k+1=12,calculate,in each case,the numerical value of k if the line PQ is parrallel to the line y=4x+7;is perpendicular to the line y=4x+7;

that sounds like a problem about "slopes" so I am looking at using the derivative, which is basically the slope of the graph.
- the equation of line PQ can be simplified to y(x) = -2kx + k -8
- derivative relative to X (k is a constant) gives you -2k
- derivative of y(x) = 4x + 7 relative to x gives you 4

if the lines are parallel then the slopes are equal:
-2k=4 gives you k = -2 => your function becomes y = 4x - 8

if the lines are perpendicular the two slopes multiplied together give you -1:
-2k * 4 = -1 gives you k=1/8 => function becomes y = -1/4x - 7/8 or in other words y = -(2x+7)/8

I have made graphic representation and it looks to be correct.
I hope it makes sense.

Apr 12, 2017 | Homework

1 Answer

What is the meaning of perpendicular lines

Parallel lines are lines that go on forever and never cross. In mathematics terms, they have the same slope, but different y-intercepts. For example, y= 3x + 5 and y=3x +7 are parallel lines.

Perpendicular lines are lines that intersect each other at 90 degrees or at right angles. If y=5 and we are looking for a line that intersects it at 90 degrees (or right angles), the line would be x= 4.

Another example would be y = x. The perpendicular line would be y = -x.

To find the perpendicular line, the slope will be the negative reciprocal. For example, y = 3x + 5, the line perpendicular would be y = - 1/3 x + b.

Another way of looking at this is if you take the slopes of the two line and multiply them, you should get -1.

Let me know if you have any questions.

Good luck.


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What is the defination for parellel lines

I linked a wiki page below.
Basically what is meant by parallel lines is two lines on the same plane that would never cross no matter how long they were in either direction.

Parallel geometry

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3x-7y=2 is an equation of a line. That line doesn't go through the point (6, -7) though. Are you looking for the equation of a line through the point parallel to the first line? Perpendicular?

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What are perpendicular lines

Two lines are perpendicular if they belong to the same plane and intersect (cut) one another at right angle. They make a 90 degree angle. If you are doing analytic geometry, two lines are perpendicular if the product of their slopes ia equal to -1.
Other relative positions of lines are parallel (they have the same slope/direction) or they are just secant at an angle not equal to 90 degrees.

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Probably a better way to say it would be parallel or perpendicular. Parallel is open, perpendicular is closed.

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