Use AB←→ and CD←→ to answer the question. AB←→ contains the points A(2,1) and B(3,4). CD←→ contains the points C(−2,−1) and D(1,−2). Is AB←→ perpendicular to CD←→? Why or why not?

Question

its a geometry equation and frankly i dont understand a thing about geometry so if someone could pls explain how they got the answer that would be great

Answer 1

In order to answer this question, you need to first understand parallel and perpendicular lines and the slope formula.

1. Parallel lines have the same slope because the go in the same direction and will never cross paths or intersect. Like train tracks for the most part.
2. Perpendicular lines have slopes that are opposite of each other. We call this negated(different signs), reciprocals (flip the fraction).
3. The formula for a slope of a line is m=(y₂-y₁)/(x₂-x₁) where the (x₁,y₁) is the 1st set of coordinates and the (x₂,y₂) is the second set of coordinates. Then we simplify the results

Now we can answer this question:

1. Find the slope of each line
2. A(2,1) and B(3,4)
3. label the x's and the y's as shown in step 3 above.
4. plug into the slope formula
5. (4-1)/(3-2) = 3/1 = 3 so m=3 for line AB
6. C(-2,-1) and D(1,-2)
7. label
8. plug into the slope formula
9. (-2-(-1))/(1-(-2)) *don't loose the subtraction sign from the original formula
10. (-2+1)/(1+2) = -1/3 so m=-1/3 for line CD
11. Since the slopes are negated (different signs), reciprocals (flipped fractions) of each other then we can say that line AB is perpendicular to line CD