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Determine whether the lines through each pair of points are parallel, perpendicular, or neither. See Example 8.$(5,3)$ and $(1,4)$$(-3,-4)$ and $(1,-5)$...

Question

Determine whether the lines through each pair of points are parallel, perpendicular, or neither. See Example 8.$(5,3)$ and $(1,4)$$(-3,-4)$ and $(1,-5)$

Determine whether the lines through each pair of points are parallel, perpendicular, or neither. See Example 8. $(5,3)$ and $(1,4)$ $(-3,-4)$ and $(1,-5)$



Answers

Determine whether the lines through each pair of points are parallel, perpendicular, or neither. See Example 8. $(5,3)$ and $(1,4)$ $(-3,-4)$ and $(1,-5)$

Here. We want to determine if the lines through these two pairs of points are parallel. Perpendicular knees, you hear, Starting with left, I need to find ourselves. So to find our soap, we take nine minus negative seven over 15 minus tall. Subtract R Y values in the numerator subject or exercise in the phenomena. Nine. Minus native. 7 16 15 miles, 12 is three and so the slope of the line through those two points in 16/3. Here on the right to find our so again in the numerator, we subtract R Y coordinates and they get a four minus negative. 20 Instructor X accordance on the bottom. Get a four. My stay of 2016 eight minus five is three, so we get 16 overthrew. So because we have the same slope on each of those that tells us that they're parallel

You probably want to determine if these two lines are parallel, perpendicular or neither. So it means we need to find each of their slopes. So let's put them into soap intercept for And so we have five wise equal to negative two X minus seven. Divide everything here by five. So why is negative? Two fists X minus 7/5. So there we have that line and soap intercept for but this other line, we also subtract five X that's a negative to wise, equal and negative. Five x plus one. Divide everything my negative, too. And so we get wise equal a positive five halves X minus 1/2 Now notice. Our slope on the left is negative. Two fists. Our soap on the right is positive. Five halves. They are opposite reciprocal, so it means these lines are perpendicular.

For this question were given two lines, so were given long. One which is ghosted. Appoints 15 9 and 20 gets up in like two, which was two points, anything before and 5 to 20. So first, the we is finish soap. I always heard First Slope is equal to nine minus stage or seven over 15 minus 12 which is equal to, Let's see, we have 16/3. Next, we have her second slope, which is equal to nearly four minus 9 20/8 to minus five, which is equal to 16/3. And so then because they have the same so we can say that the pair of lines are parallel.

For this question were given two lines to explicit by wise people to 97 5 x must to why, you see, what's the one? We're us a terminus of Lines are parallel port particular were neither. So to start off with, we can write this and some interesting for him to get it. If I wanted to go to think of two X minus seven. Gets wise. You pretending you're 2/5 X minus 7/5. The other side we have about. So we have to. Why? It's able to fire X minus one. Yes, wise it with your 5/2 X minus 1/2. So, based on our two slopes, we know that these two lines are perpendicular.


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