Vectors: Which of the following equations represent the line?

[HugeLag]

Suppose a 2D line passes through two points P0(10, 15) and P1(200, 20). Answer Questions 7 * 10 regarding this line.

Which of the following equations represent the line?

5x - 190y +2800=0?

5x + 6y -8=0?

(x-10, y-15)•(-5, 190)=0?

(x-200, y-20)•(5, -190)=0?

I worked this out using m=y2-y2/x2-x1

My answer was

y=1over38x+14 14over19

This seems wrong, because it does not match with the answers given in the question? This is in relation to the points P0 (10,15), and P1(200,20)

 

[Deleted member 4993]

Suppose a 2D line passes through two points P0(10, 15) and P1(200, 20). Answer Questions 7 * 10 regarding this line.

Which of the following equations represent the line?

5x - 190y +2800=0?

5x + 6y -8=0?

(x-10, y-15)•(-5, 190)=0?

(x-200, y-20)•(5, -190)=0?

I worked this out using m=y2-y2/x2-x1 ..... incorrect on two counts

My answer was

y=1over38x+14 14over19 → \(\displaystyle y = \frac{1}{38} * x + 14\frac{14}{19}\) → same as my answer after I deciphered your answer

This seems wrong, because it does not match with the answers given in the question? This is in relation to the points P0 (10,15), and P1(200,20)

I do not understand the last two choices given!

The answer should be:

38y - x - 560 = 0 (or some variation of that expression)

By the way, you should really learn to use grouping symbols (i.e. parentheses).

 

[pka]

Suppose a 2D line passes through two points P0(10, 15) and P1(200, 20).
Which of the following equations represent the line?nnbbb

That line is \(\displaystyle \ell : \{(10+190t,~15+5t) :t\in \mathbb{R}\}\) or \(\displaystyle \ell=\begin{array}{l} x=10+190t\\y=15+5t\end{array} \)
Note that when \(\displaystyle t=0\) we get \(\displaystyle P_0\); when \(\displaystyle t=1\) we get \(\displaystyle P_1\)

Now solve for \(\displaystyle t\)
\(\displaystyle \begin{align*}\dfrac{x-10}{190}&=\dfrac{y-15}{5}\\5x-50 &=190y-2850\\5x-190y&=-2800\end{align*}\)