Distance Between Parallel Lines Steps ( Formula order) Example Number One: Parallel Lines:

4x+4=y

4x-4=y Parallel Lines Parallel lines will never intersect and have the same slope Perpendicular lines See? They have the same slopes. Intersect at a right angle the slopes are opposite reciprocals Slope Rise Perpendicular Line: Find the inverse and switch the signs for the normal slope to find the slope of the perpendicular line.

In this case, the slope of the perpendicular line would be -1/4.

So far, we have y=-1/4x+b as the equation for the perpendicular line. Run How steep a line is Horizontal lines have a slope of zero Point-Slope y-y1=m(x-x1) Distance Formula Next, we will take the coordinate for the y-intercept of one of our parallel lines, and insert it into our equation for the perpendicular line, using the x-coordinate for x, and the y-coordinate for y. 4=-1/4(0)+b (x-x1)^2 + (y-y1)^2 That cancels the -1/4 out, telling us that b=4. Substitution Step 1: So, our finished equation for the perpendicular line, is y=-1/4x+4. Use information you already have and plug it into an algebraic expression to get an answer to a problem x=4

y=4x+3

y=4(4)+3 Next, we will set the perpendicular line's equation equal to the equation of the parallel line we didn't use the y-intercept of. So, -1/4x+4 = 4x-4 Make a Perpendicular equation First graph the two equations find the opposite reciprocal of your slope. For example if your slope is 3 then your opposite reciprocal is -1/3. Once you have your opposite reciprocal you will plug in one of your points and substitute where you will get your y-intercept. Step 2: Using the slope-intercept form of a parallel line change the slope to the opposite reciprocal When we work the equation out to find x, we find that x=32/17 NO! IT IS NOT JUST COUNTING SQUARES. By: Megan Gavel, Emily Neel and Kara Taylor Parallel-y=2x+3

Perpendicular-y+(-1/2)x+3 Slope-intercept y=mx+b Now, we are going to substitute 32/17 as x, into the perpendicular line equation to find y. m-slope

b- y intercept We find out that y=60/17. So we now know that we have two sets of coordinates:

(0,4) and (32/17, 60/17) Now use a system of equations to determine the point of intersection Step 3: Next, substitute the coordinates into the distance formula. Vocab (32/17-0)^2+(60/17-4)^2 (32/17)^2+(-8/17)^2 1024/289+64/289 Now plug in both of your coordinates in to the distance formula which is:

√(x- x)² + (y- y)² Step 4: 1088/289 Our final answer is: 1.94! Example Number Two: Parallel Lines:

y=2x+2

y=2x-3 Perpendicular:

y=-1/2x+b Step 5: Solve! You will now get your answer! 2=-1/2(0)+b 2=b Finished Perpendicular Line:

y=-1/2+2 -1/2x+2=2x-3

x=2 y=-1/2(2)+2

y=1 (2-0)^2+(1-2)^2 (2)^2+(-1)^2 Doing the Distance Formula 4+1 5 The Final Answer is:

2.24 A graph Graph For Example One: Parallel lines always have the same distance between them y=4x+4 y=4x-4 y=-1/4x+4 y=2x+2 y=2x-3 y=-1/2x+2 Perpendicular A perpendicular line is the shortest distance between two parallel lies

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# Distance Between Parallel Lines

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