How do I find out if a line is parallel, perpendicular, or neither using 2 given points?

Since it's due "tom", you should probably follow guidelines in "read before posting" to get help as soon as possible.
 
Btw this is due tom
To sanshar: if you really want expert help then use completely standard English.
Many of us do not understand the degraded ignorant web-speak.
If we cannot understand the post how can we help you?
 
Two lines are parallel only if their slopes are both equal or both are undefined.
Two lines are perpendicular only if the product of their slopes is -1 OR one slope is 0 and the other slope is undefined.
Now compute the slopes!
 
Re the title to your post: "How do I find out if a line is parallel perpendicular or neither using 2 points". Many people will throw up their hands in despair at that! A single line is NEVER "parallel perpendicular or neither". Those are properties of two or more lines.

Since "tom" is already well past (we buried him two days ago) I have no qualms about answering. You are, fortunately, given two lines, AB and CD. A is (2, 3) and B is (2, 6). Since those points have the same "x" value, 2, that is a vertical line. If you were to try to find the slope you would get (6- 3)/(2- 2)= 3/0 which is impossible. The line has NO slope. (Some people might say the slope is "infinity". I would not.)

C is (-1, 0) and D is (3, 3). That line has slope (3- 0)/(3- (-1))= 3/4. CD is not vertical (since it has no slope) so the lines are NOT parallel. CD is not horizontal (since its slope is not 0) so the lines are not vertical. They are "neither".
 
C is (-1, 0) and D is (3, 3). That line has slope (3- 0)/(3- (-1))= 3/4. CD is not vertical (since it has no slope) so the lines are NOT parallel. CD is not horizontal (since its slope is not 0) so the lines are not vertical. They are "neither".

CD is not vertical (since it has a slope) so the lines are NOT parallel. CD is not
horizontal (since its slope is not 0) so the lines are NOT perpendicular. Therefore,
they are "neither."
 
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